Research ArticleOrganic Food Labeling and Advertising A TripartiteGame Model between One Supplier and TwoHeterogeneous Manufacturers

Jun Wang 1 Song Yao 1 Xinman Lu 1 and Yu Li 2

1School of Management Science and Engineering Tianjin University of Finance and Economics Tianjin 300222 China2Coordinated Innovation Center for Computable Modeling in Management ScienceTianjin University of Finance and Economics Tianjin 300222 China

Correspondence should be addressed to Yu Li liyutjufeeducn

Received 23 June 2019 Revised 15 September 2019 Accepted 23 September 2019 Published 5 November 2019

Academic Editor Dehua Shen

Copyright copy 2019 Jun Wang et al shyis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

shye development of the organic food industry is of great signicance to the environment and society as consumers increasinglyprefer green and healthy food However certain production and investment problems must be solved A tripartite game model isestablished in this study to investigate the labeling and advertising investment decisions in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by the biform game approach In addition a subsidy mechanism isintroduced to alleviate underinvestmentshye results show that rst the supplier will label if labeling cost is relatively low withoutconsidering advertising investment Second the supplier will not label if advertising investment is considered because of theldquodiusion of responsibilityrdquo mentality and both manufacturers will invest in advertising as a result of equilibrium in dominantstrategies shyird the advertising subsidy mechanism can achieve Pareto improvement and coordinate the supply chain Finallymanufacturer heterogeneity will lead to dierentiated subsidy strategies that the supplier can claim to give additional subsidies tothe weak manufacturer thereby weakening the ldquodiusion of responsibilityrdquo mentality

1 Introduction

Environmental problems attract increasing attention as theeconomy develops [1] Conversely the quality of food isdeclining [2] and the harmfulness of unhealthy food isgradually increasing [3] Organic food is considered envi-ronmentally friendly [4] and can reduce harm to the en-vironment [5] Against this background organic food formsa market with good development prospect in the global foodindustry [6ndash8] On one hand many governments attachgreat importance to organic food production and improvepolicies to promote the development of this industry [9 10]For example the Russian government implements a bill thatprohibits the use of pesticides and antibiotics to regulate theproduction of organic food in Russia On the other handconsumersrsquo low-carbon preference and environmentalawareness promote green investment among enterprises

[11] Many enterprises produce or sell organic food toimprove market competitiveness For example WholeFoods Market is the largest organic supermarket chain andthe rst certied organic food retailer in the United StatesAlthough its price is slightly higher than those of othersupermarkets it remains very popular with consumersespecially among families with children

We study the decisions of supplier and manufacturers inthe noncooperative stage and prot allocation in the co-operative stage in an organic food supply chain In thenoncooperative stage two manufacturers decide whether ornot to invest in advertising while the supplier decideswhether or not to label the goods In the cooperative stageprots will be allocated by the Shapley value method shyecooperative game method is generally used in the organicfood supply chain However when considering investmentobtaining a rational decision is dicentcult if only the

HindawiComplexityVolume 2019 Article ID 3143416 14 pageshttpsdoiorg10115520193143416

cooperative game method is used because the investmentproblem should be analyzed in the noncooperative stage[12] Fortunately the biform game can solve such problemseffectively Based on the cooperative game the biform gameconsiders the noncooperative game method and divides thegame process into two stages for analysis [13] With thisapproach Feess and +un [12] distinguished two stages inthe process of solving the supply chain problem Enterprisescan invest in the first stage and divide profit in the secondstage +e result shows that this method can coordinate thesupply chain

In the cooperative stage we use the Shapley valuemethod to calculate the expected profits of the supplier andmanufacturers in various scenarios and provide optimaldecision suggestions by comparing and analyzing profits+e Shapley value method is commonly used to allocateprofit to members Researchers have widely used the Shapleymethod in the cooperative game since its introduction in1953 because it can ensure fairness anonymity effectivenessadditivity and symmetry when allocating profit [14] Liuet al [15] used the Shapley value method to provide a profitallocation mechanism for enterprises in a dynamic supplychain but it requires related information from each firm ateach time point Gao et al [16] improved the Shapley valuemethod to ensure fair profit distribution when two collab-orators cooperate under uncertain profit However theShapley value method has several limitations First it doesnot take into account the effort of each enterprise Instead itonly considers the marginal contribution of each memberSecond it supposes that all enterprises bear the same riskbut certain factors such as ecological technology level andrisk will also affect profit allocation In view of this contextXu et al [17] took into account the environmental effort leveland risk to improve the Shapley value method

Ecolabeling which can identify the green attributes offood has been used in the food market to attract consumersrsquoattention Labeling products can increase the reference pricein the minds of consumers and improve the environment toa certain extent [18] +erefore many organic food suppliersare willing to increase the greenness and place green labelson their products to increase value and improve competi-tiveness [19 20] However producing and processing or-ganic products are costly [21] because improving productiontechnology and organic certification brings additional ex-penses to food suppliers +erefore deciding if productsshould be labeled is an important decision for food suppliers+is study assumes that labeling can dictate a premium price[22] and generate labeling costs that will be borne by thesupplier According to the expected profits calculated usingthe Shapley value method the supplier will decide whetheror not to label in the noncooperative stage (Section 31)

Advertising is crucial in attracting consumers and in-creasing market demand to a certain extent [23 24] Manyenterprises frequently invest in advertising to further buildgoodwill and brand reputation thus improving competi-tiveness in the market [25] +erefore the optimal adver-tising investment schemes of supply chain members arewidely studied For example Hong et al [26] established aStackelberg game model and found that advertising has an

important impact on market demand and profits of channelmembers it can also coordinate supply chain memberseffectively [27] Wu et al [28] compared the optimal ad-vertising strategies in decentralized and centralized sce-narios by the differential game method and concluded thatthe scheme under centralized decision-making can increasethe advertising investment of supply chain membersHowever investing advertisement requires correspondingcost +erefore reducing advertising costs to maximizecorporate profits has become a research hotspot for businessoperators and scholars In the majority of cases this problemcan be solved effectively by using the cooperative advertisingstrategy which can stimulate the advertising investmentlevel and increase the performance of supply chains to helpmembers achieve Pareto improvement Horizontal andvertical cooperative advertising are the two commonmethods used in cooperative advertising In the horizontalcooperative advertising scheme retailers at the same saleslevel jointly advertise Gou et al [29] studied joint ventureand contract alliance cooperative schemes by the differentialgame method and found that both schemes are superior tothe noncooperative one In the vertical cooperative adver-tising scheme the manufacturer will bear part of the ad-vertising cost to stimulate the retailerrsquos advertisinginvestment [30] Lu et al [31] studied the equilibriumstrategy when the manufacturer provides the retailer withadvertising subsidy and found that the negotiated adver-tising subsidy rate can achieve Pareto optimum Accordingto De Giovanni et al [32] the retailer may no longer bewilling to cooperate when the manufacturerrsquos revenue shareis too high On the basis of these studies other scholarsfurther examined the comprehensive cooperative advertis-ing scheme Xiao et al [33] proposed a hybrid program thatinvolved the vertical and horizontal cooperative advertisingschemes in which manufacturers and retailers jointly makeupstream and downstream decisions for the allianceChernonog and Avinadav [34] compared three cooperativeadvertising schemes where the responsibility of advertisinginvestment is shared by the manufacturer retailer or boththey found that the scheme in which the manufacturer is thesole advertising investor is a complete disclosure mecha-nism Li et al [35] explored three cooperative advertisingmodes namely unilateral cooperation bilateral co-operation and integrated modes +e authors found that incontrast with the unilateral cooperation mode the bilateralcooperation mode can bring additional benefits to an entirechannel In the current work a tripartite game model isestablished to investigate further the impact of manufacturerheterogeneity on investment decisions

We assume that two manufacturers exist One is wellknown in the food industry and has rich experience inorganic food production whereas the other is an emergingfood manufacturer with relatively low reputation +esupplier can supply raw food materials to only one man-ufacturer creating a competitive environment for the twomanufacturers Each manufacturer decides whether or notto invest in advertising and to what level (Section 32) Wefirst establish the branded ingredient game model whichonly considers the labeling decision of the supplier +e

2 Complexity

advertising investment game model which studies not onlythe labeling decision of the supplier but also the investmentdecision of manufacturers is established to determine theinfluences of advertising investment on the decisions ofplayers

Underinvestment may occur in advertising investmentbecause of the costs and risks Subsidy for investment costscan alleviate the underinvestment problem [12] +is studyintroduces an advertising subsidy mechanism wherethe supplier commits to pay a certain percentage of themanufacturersrsquo advertising investment In the non-cooperative stage the supplier decides on the subsidypercentage and whether or not to label the product In thecooperative stage surplus is divided according to theShapley value +e optimal subsidy percentage can beobtained via backward induction (Section 33) Manyscholars focused on the subsidy problem in supply chainsConsidering the investment problem of supply chainsProch et al [36] built a continuous time model and foundthat the supplier can encourage manufacturers to raise theirinvestment level by subsidizing a portion of their in-vestment costs to improve the underinvestment problemIn contrast to Proch et al [36] Alaei and Setak [37]proposed that subsidy negotiation can further improveadvertising performance by establishing and analyzing thedynamic differential game model In addition manyscholars proposed that subsidy is not confined to one-waysubsidy In certain conditions two-way subsidy is superiorto one-way subsidy For instance Song et al [23] in-troduced a two-way subsidy mechanism where the mem-bers of the supply chain can share investment costs withone another to coordinate the supply chain However theexisting literature on subsidy seldom considers manufac-turer heterogeneity As such we establish a tripartite gamemodel with advertising subsidy to study the optimal sub-sidy strategy of the supplier when faced with differentiatedmanufacturers and to alleviate underinvestment

+is study has the following key contributions to theexisting literature on competition and cooperation in or-ganic food supply chains First it provides optimal strategiesin labeling and advertising investment with consideration ofmanufacturer heterogeneity and consumer green preferenceIt presents interesting and unique explanations for severalphenomena Second it verifies the existence of un-derinvestment and introduces a further coordination pro-gram namely the advertising subsidy mechanism toalleviate the problem and achieve the Pareto improvement tocoordinate organic food supply chains Moreover it offersreasonable suggestions on the supplierrsquos subsidy andmanufacturersrsquo advertising investment In fact the optimaldecisions of enterprises will enhance their competitivenessin the highly competitive market [38]

+e remainder of this paper is structured as followsSection 2 presents the notations and assumptions Section 3describes and analyses the tripartite game model Section 4provides the numerical analysis Finally Section 5 concludesand summarizes the management insights and future di-rections of this study

2 Notations and Assumptions

First we provide several essential notations as follows

Pi highest price that consumers will pay for manu-facturer irsquos products where i isin AB

c0 labeling cost incurred by the supplierrsquos labelingstrategyci advertising cost incurred by manufacturer irsquos in-vestment in advertisement where i isin AB

αi investment return coefficient where i isin AB

πki profit of manufacturer i at the end of the co-operative stage where i isin AB and k takes values of 12 and 3 in the branded ingredient gamemodel (BIGM)advertising investment game model (AIGM) and ad-vertising subsidy mechanism (ASM) respectivelyπkM profit of the supplier at the end of the cooperativegame stage where k takes values of 1 2 and 3 in theBIGM AIGM and ASM respectivelyti supplierrsquos subsidy percentage for the manufacturerrsquosadvertising investment where i isin AB

Based on these notations we propose the followingassumptions to simplify the model

(1) +e production cost of the supplier is 0(2) Labeling cost is entirely borne by the supplier

whereas the advertising cost is entirely borne by themanufacturers

(3) +e sales volume is 1(4) Labeling does not affect the product of well-known

manufacturer A and increases the price of theproduct of manufacturer B by αBc

(12)0 [12] where

PB + αBc(12)0 ltPA

(5) Advertising and labeling are the same type of in-vestment that is for each manufacturer the in-vestment return coefficients of labeling andadvertising are equal which are expressed as αi andαA αB respectively

For convenience the definitions used in the followingsections are listed in the following paragraphs First weintroduce the meaning of certain symbols in the gameprocess In gamer set N 1 2 n each player j selectsstrategy sj isin Sj where Sj represents the strategy set ofplayer j Strategy vector (s1 sn) defines a utilitytransferable game and the corresponding characteristicfunction is defined as v(s1 sn) 2N⟶ R where 2N isthe power set of N In this study N MAB For any setC isin 2N v(s1 sn)(C) represents the revenue createdjointly by players in set C where v(s1 sn)(empty) 0 Onthis basis we set the following definitions accordingto [13]

Definition 1 In gamer set N a noncooperative game isdefined as (S1 Sn) whereas (N v) denotes cooperativegame +e biform game is defined as (S1 Sn N v)

Complexity 3

Definition 2 In cooperative game (N v) the Shapley valueof each player j is

ϕj(v) 1

|N|1113944

CsubN∖ j

|N| minus 1

|C|

⎛⎝ ⎞⎠

minus 1

(v(Ccup j1113864 1113865) minus v(C))

(1)

where |N| represents the number of all members in gamerset N |C| denotes the number of members in any subset C in

N and |N| minus 1|C|

1113888 1113889 refers to the number of combinations of

|C| elements taken from |N| minus 1 different elements

Definition 3 If any two alliances namely C1 and C2 satisfyC1 capC2 empty and

v C1 cupC2( 1113857ge v C1( 1113857 + v C2( 1113857 (2)

then the cooperative game (N v) is superadditive

3 Model Description and Analysis

+e tripartite game model proposed in this study consists ofthree parts namely BIGM AIGM and ASM which are usedto investigate the optimal strategy of labeling advertisinginvestment and subsidy respectively in organic food supplychains

First we establish the BIGM which only considers thelabeling decision of the supplier In this model the supplierrsquosstrategy set is SBIGMM Labeling No labeling +e AIGM isthen established to explore further the optimal decision of thesupplier regarding advertising investment and its impact thelabeling decision of the supplier and advertising investmentdecision of manufacturers +e AIGM involves the com-petitive game between manufacturers and cooperative gamebetween the supplier and manufacturers In this model thestrategy sets of the supplier and manufacturers areSAIGMM Labeling No labeling and SAIGMi Advertising Noadvertising respectively where i isin AB Finally to alleviateunderinvestment and coordinate the organic food supplychain we establish the ASM to elucidate further the influenceof subsidy In this context the strategy sets of the supplier andmanufacturers are SASMM Labeling No labelingtimes Sub-sidizing No subsidizing and SASMi Advertising No ad-vertising respectively

31 BIGM We assume that manufacturers A and B producethe same kind of organic food in the supply chain andsupplier M can supply raw materials to only one manu-facturer due to financial constraints Manufacturer A is awell-known manufacturer with rich experience in organicfood production whereas manufacturer B is an emergingfood manufacturer with relatively low reputation Con-sumers are willing to buy manufacturer Arsquos product at pricePA andmanufacturer Brsquos product at price PB where PB ltPAdue to the brand effect Figure 1 depicts the decision se-quence of the players in the BIGM

+e first stage is the noncooperative stage where sup-plier M decides whether or not to label the product asldquoorganic foodrdquo at cost c0 According to Assumption (4) inSection 2 labeling will bring investment returns αBc

(12)0 to

manufacturer B but no price premium to manufacturer Arsquosproduct as shown in Figure 2

+e optimal decision of supplier M is dependent on thecomparison and analysis of its expected profits under var-ious scenarios Figure 3 illustrates the income range ofsupplier M When supplier M opts not to label and to co-operate with manufacturer A the total revenue is PAwhereas manufacturer B gains zero benefit If supplier Mcooperates with manufacturer B then the total revenue is PBand PB＜PA +us the income range of supplier M in thiscase is [PB PA] Supplier M will prepay labeling cost c0 whenit decides to label the product If supplier M cooperates withmanufacturer A then the total revenue will be PA minus c0However if supplier M cooperates with manufacturer Bthen the total revenue will be PB + αBc

(12)0 minus c0 +erefore

the income range of supplier M in this case is [PB + αBc(12)0 minus

c0 PA minus c0]In the cooperative stage the supplier cooperates with

one manufacturer to produce and sell organic food andultimately gain profit At the end of the cooperative stage thesupply chain use the Shapley value method to divide profitNotably the manufacturerrsquos final profit is defined as πjwhere πj ϕj(v) j isin AB the final profit of supplier M isπM where πM ϕM(v) minus c0Γ We use indicator function Γ

1 if supplier M chooses to label and Γ 0 otherwise Byanalyzing the supplierrsquos final profit we can obtain its optimaldecision

Proposition 1 Only when the labeling cost is relatively lowwill the supplier choose to label Table 1 presents the supplierrsquosoptimal decision in the BIGM

Proof First we analyze the income range of supplier M Ifsupplier M opts not to label then the income range is[PB PA] otherwise the income range is [PB + αBc

(12)0 minus

c0 PA minus c0] Only when PB + αBc(12)0 minus c0 gtPB will supplier

M consider labeling that is

c0 lt α2B (3)

+en we use the Shapley value method to calculate thesupplierrsquos profit when choosing to label or not and use πL

1Mand πN

1M to express both decisions respectively as shown inTable 2 We find that when πN

1M lt πL1M namely

c0 lt136α2B (4)

supplier M will choose to label whereas it will not labelwhen c0 ge (136)α2B Notably the supplier decides not tolabel when the profits of labeling and no labeling are thesame

In addition after considering the price premium ofmanufacturer Brsquos product when labeling we also take theinequality in Assumption (4) in Section 2 into account as abasic condition for supplier Mrsquos decision to label namely

4 Complexity

c0 ltPA minus PB

αB1113888 1113889

2

(5)

When inequalities (3)ndash(5) are simultaneously metsupplier M will choose to label otherwise it will forgolabeling

Referring to Proposition 1 we find that the labelingdecision of the supplier is mainly dependent on labeling costwithout considering advertising investment +e suppliershould label to achieve higher profit given that labeling costis relatively low However when the labeling cost is high

labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofit At this point the supplier should choose not to label

According to Definition 3 we will verify whether co-operative game is superadditive as follows

Proposition 2 Cooperative game (N v) is superadditive

Proof In fact the manufacturer will not profit if it does nottake the supplierrsquos resource Hence we can infer thatv( i ) v( j1113864 1113865) 0 i j isin AB If supplier M cooperateswith manufacturer i then

v( M i ) v( M i j1113864 1113865)gt 0 (6)

hence v( j1113864 1113865) + v( M i )le v( M i j1113864 1113865) +us we derive thefollowing

v C1( 1113857 + v C2( 1113857le v C1 cupC2( 1113857 (7)

As a result cooperative game (N v) is superadditive

+e superadditivity of the cooperative game shows thatall players in the game are willing to cooperate because thetotal revenue from cooperation is always no less than thesum of the revenue from their respective operations +isnotion also proves the feasibility and rationality of themodel

In this subsection we dissect the supplierrsquos labelingdecision without considering the manufacturersrsquo advertisinginvestment and verify the superadditivity of the cooperativealliance Next we will establish the AIGM to further studythe investment decisions of the supplier and manufacturerswhen considering advertising investment

32 AIGM To increase competitiveness the manufacturerswill advertise their products On the basis of the BIGM weestablish the AIGM to further study the impact of adver-tising investment on the decision of supply chain membersWe assume that manufacturers A and B have the ability toadvertise their products Figure 4 shows the prices of themanufacturersrsquo products in the BIGM and AIGM

Supplier M decideswhether to label

Manufacturer goesinto production

Noncooperative stage Cooperative stage

Supplier and manufacturerdivide profit

Figure 1 Decision sequence of players in BIGM

Supplier MA B

0 0

0 0

No label

PA

PAPB + αBc0

(12)

PB

Label

A B

Figure 2 Prices of manufacturersrsquo product in BIGM

Supplier M

No label

Label

[PB PA]

[PB + αBc0(12) ndash c0 PA ndash c0]

Figure 3 Income range of supplier M in BIGM

Table 1 Supplierrsquos optimal decision in BIGM

Condition Decisionc0 lt (136)α2B and c0 lt ((PA minus PB)αB)2 Labelc0 ge (136)α2B No label

Table 2 Expected profit of supplier M in BIGM

SM π1MNo label πN1M (12)PA + (16)PBLabel πL1M (12)PA + (16)(PB + αBc

(12)0 ) minus c0

Complexity 5

In the noncooperative stage (S1 Sn) supplier Mdecides whether to label whereas manufacturers A and Bdecide whether to invest in advertising and how much toinvest In the cooperative stage (N v) the supplier andmanufacturers divide the profit Figure 5 illustrates thedecision sequence in the AIGM

In the analysis of the biform game (SA SB SM N v) weadopt the backwards induction which is contrary to thedecision order First profit set (πA πB πM) under strategyset (SA SB SM) is calculated using the Shapley valuemethod+en the optimal decision of the manufacturer onadvertising investment is obtained by analyzing theseprofits Finally we obtain the labeling decision of thesupplier

Figure 6 provides the income ranges of supplierM In thecase of manufacturers A and B investing in advertising ifsupplier M chooses not to label and cooperates withmanufacturer A then the total revenue is PA + αAc

(12)A minus cA

and manufacturer B gains no benefit However if supplier Mcooperates with manufacturer B then the total revenue isPB + αBc

(12)B minus cB +us the income range of supplier M in

this case is [PB + αBc(12)B minus cB PA + αAc

(12)A minus cA] If supplier

M chooses to label and cooperates with manufacturer Athen the total revenue will be PA + αAc

(12)A minus c0 minus cA If

supplier M cooperates with manufacturer B then the totalrevenue will be PB + αB(c0 + cB)(12) minus c0 minus cB In this casethe income range of supplier M is [PB + αB(c0 + cB)(12)minus

c0 minus cB PA + αAc(12)A minus c0 minus cA]

Notably however if one or both manufacturers do notinvest in advertising the supplierrsquos income range will be-come more complex Consequently we will analyze theinvestment decisions of the manufacturers

Proposition 3 Manufacturers A and B choose to invest inadvertising in AIGM

Proof When supplier M chooses not to label we can obtainthe profit of manufacturer B using the formula in Definition2 as follows

πN2B 16

PB + αBc(12)B1113872 1113873 minus cB (8)

Understanding that manufacturer Brsquos profit is only re-lated to its investment is easy that is advertising investmentcan bring positive net income to B +us manufacturer Bwill choose to invest in advertising +en we analyze Arsquosinvestment decision as follows

πN2A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus cA (9)

Under the premise that manufacturer B must invest inadvertising advertising investment can also bring positive netincome to manufacturer A who will also invest in advertisingat this moment +erefore manufacturers A and B will investin advertising when supplier M chooses not to label

Similarly when supplier M chooses to label we obtain

πL2B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cB

πL2A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cA

(10)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in AIGM

Proposition 3 indicates that both manufacturers shouldactively invest in advertising to strengthen competitivenessin the face of the existence of a competitor which equalsequilibrium in the dominant strategy by the competitivegame between two manufacturers Notably howeveroverinvestment may adversely affect manufacturers becauseexcessive investment will not only reduce the manufacturersrsquoshort-term operating capital but also damage profit and leadto bankruptcy +erefore manufacturers should furthermake a decision on the optimal levels of advertising in-vestment namely clowastA and clowastB In the following discussion wewill highlight each manufacturerrsquos optimal advertising in-vestment level under various strategies

Proposition 4 Table 3 presents the optimal amount of eachmanufacturerrsquo advertising investment

Proof We can obtain the manufacturersrsquo expected profitunder the different decisions of supplier M using the Shapleyvalue method When supplier M chooses not to label we canderive cNlowastA (116)α2A and cNlowastB (1144)α2B by calculatingdπN

2AdcA 0 and dπN2BdcB 0 respectively Similarlywhen M chooses to label we can obtain cLlowastA (116)α2A andcLlowastB (1144)α2B minus c0

Analysis of the manufacturersrsquo optimal advertising in-vestment level indicates that manufacturer heterogeneity can

A B

0 0

0 0

No label

Label0 0

0 0

No label

Label

A B

AIGM

BIGM

PA

PA

PB

PA + αAcA(12)

PA + αAcA(12)

PB + αB(c0 + cB)(12)

PB + αBcB(12)

PB + αBc0(12)

Figure 4 Prices of manufacturersrsquo products in BIGM and AIGM

6 Complexity

lead to differentiation of investment decisions +e supplierrsquosdecision to label has no effect onmanufacturer Arsquos investmentbut reduces manufacturer Brsquos investment According to As-sumption (4) in Section 2 labeling does not change the priceof manufacturer Arsquos products and will not thus affect man-ufacturer Arsquos decision However supplierMrsquos decision to labelwill increase the price of manufacturer Brsquos products whichindicates that the supplier partially undertakes the re-sponsibility that jointly improves the value of the products Inthis manner manufacturer Brsquos view that is ldquodiffusion ofresponsibilityrdquo is triggered and can be used to denote thepsyche of one who wants to decrease his responsibility at theexpense of the partnerrsquos efforts+erefore manufacturer Bwillreduce his investment level when supplier M chooses to labelHorizontally regardless of whether the supplier decides tolabels or not the well-known manufacturer will always investmore in advertising compared with the weaker manufacturerbecause the well-known manufacturer wants to consolidatecompetitiveness and attractsmore attention from the supplierIn summary the weaker manufacturer should appropriatelyreduce its investment in advertising when the supplier choosesto label whereas the well-known manufacturer should retainits investment level to be always higher than that of the weakermanufacturer to solidify its market position andcompetitiveness

We will further discuss the supplierrsquos decision to label inthe face of the manufacturersrsquo equilibrium strategies

Proposition 5 Considering advertising investment supplierM always chooses not to label

Proof According to Table 4 we find that πN2M minus πL

2M c0 gt 0+erefore supplier M who pursues maximum profit alwaysopts not to label

From the perspective of the individual interests of de-cision makers and in the face of the manufacturersrsquo in-vestment efforts the supplier will generate the ldquodiffusion ofresponsibilityrdquo mindset and choose not to label to minimizeits investment From the perspective of the overall interest ofthe supply chain when the manufacturers contribute to thecooperative alliance through advertising investment thesupplierrsquos active investment behavior that it still chooses tolabel may let the total investment outweigh the total returnand enter the stage of diminishing returns on scale Intheory the competitive game equilibrium result that allmanufacturers invest in advertising improves the supplierrsquosadvantage in the cooperative game which leads to the co-operative game equilibrium result where the supplier doesnot need to label

In this subsection we set up the AIGM and use theShapley value method to calculate the profit of each playerunder different scenarios and finally obtain optimal de-cisions by backwards induction Finding shows that in thetripartite game with advertising investment between onesupplier and two heterogeneous manufacturers the lattershould invest in advertising to enhance competitivenessand the possibility of cooperation with the supplier Doingso will contribute to improving the value of products suchthat the supplier does not need to label In the followingsubsection we will verify the existence of the un-derinvestment problem and further shed light on theoptimal decisions of the supplier and manufacturers inASM

33 ASM +e supplier usually gives the manufacturers anincentive policy to stimulate investment In this subsectionwe introduce the advertising subsidy mechanism where thesupplier will commit to pay a certain percentage of themanufacturersrsquo advertising investment Figure 7 providesthe decision sequence in ASM

For ease of distinction we denote π2j and π3j to rep-resent the profit of j in the AIGM and ASM respectivelywhere j isin MAB ti refers to the supplierrsquos subsidy per-centage for the manufacturerrsquos advertising investment

Supplier M decideswhether to label

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decidewhether to investin advertising and

how much to invest

Figure 5 Decision sequence of players in AIGM

Supplier M

No label

Label

[PB + αBcB(12) ndash cB PA + αAcA

(12) ndash cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash cB PA + αAcA(12) ndash c0 ndash cA]

Figure 6 Income ranges of supplier M in AIGM

Table 3 Optimal amount of advertising investment

SM clowastA clowastB

No label (116)α2A (1144)α2BLabel (116)α2A (1144)α2B minus c0

Table 4 Expected benefits of supplier M in AIGM

SM π2MNo label πN2M (12)PA + (16)PB + (18)α2A + (172)α2BLabel πL2M (12)PA + (16)PB + (18)α2A + (172)α2B minus c0

Complexity 7

+erefore we can express the advertising subsidy mecha-nism as follows

π3A π2A + tAcA

π3B π2B + tBcB

π3M π2M minus tAcA minus tBcB

(11)

Considering the effect of subsidy on earnings based onthe AIGM we obtain the income range of the supplier inASM as shown in Figure 8

Using the same method of analysis in the AIGM weobtain the optimum decisions of the supplier and manu-facturers First we analyze whether the manufacturers willchoose to invest in advertising in ASM

Proposition 6 Manufacturers A and B choose to invest inadvertising in ASM

Proof When supplier M chooses not to label manufacturerBrsquos profits can be acquired by the Shapley value method asfollows

πN3B

16

PB + αBc(12)B1113872 1113873 minus 1 minus tB( 1113857cB (12)

Finding that manufacturer Brsquos profit is only related to itsinvestment and advertising investment can bring a positivenet income to manufacturer B is easy to understand +usmanufacturer B will choose to invest in advertising+en weanalyze manufacturer Arsquos investment decision and derive itsprofit as follows

πN3A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus 1 minus tA( 1113857cA

(13)

Under the premise that manufacturer B must invest inadvertising manufacturer A can derive positive net incomefrom advertising investment+erefore manufacturer A willalso invest in advertising

Similarly when supplier M chooses to label we have

πL3B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus 1 minus tB( 1113857cB (14)

πL3A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus 1 minus tA( 1113857cA

(15)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in ASM

We find that under the advertising subsidy mechanismthe manufacturers will still choose to invest in advertising Inaddition we can speculate that the manufacturers are morewilling to invest because the subsidy is harmless and ben-eficial to them +erefore the manufacturers may increaseinvestment under the advertising subsidy mechanism Nextwe will verify whether subsidy will promote the manufac-turersrsquo investment by analyzing the manufacturersrsquo optimalinvestment level and elucidate the optimal subsidy strategy

Proposition 7 Table 5 presents the optimal decisions ofplayers in ASM

Proof We can obtain the profit functions of the supplierunder different circumstances using the Shapley valuemethod When the supplier chooses not to label then

πN3M

12

PA + αAc(12)A1113872 1113873 +

16

PB + αBc(12)B1113872 1113873 minus tAcA minus tBcB

(16)

Otherwise

πL3M 12

PA + αAc(12)A1113872 1113873 +

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus tAcA minus tBcB minus c0

(17)

Based on equations (12)ndash(17) we can obtain the optimaldecisions of advertising investment and subsidy When Mchooses not to label we can derive cNlowastA α2A(16(1 minus tA)2)

and cNlowastB α2B(144(1 minus tB)2) from dπN3AdcA 0 and fromdπN

3BdcB 0 respectively +en we can obtain tNlowastA 13and tNlowastB 13 from zπN3MztA 0 and from zπN

3MztB 0respectively +erefore we have cNlowastA (964)α2A andcNlowastB (164)α2B

When supplier M opts to label we can derive cLlowastA

α2A(16(1 minus tA)2) and cLlowastB α2B(144(1 minus tB)2) minus c0 fromdπL

3AdcA 0 and from dπL3BdcB 0 respectively +en wehave tLlowastA 13 from zπL

3MztA 0 Based on zπL3MztB 0

we find that tLlowastB satisfies

α2B 1 minus 3tB( 1113857 + 144c0 1 minus tB( 11138573

0 (18)

Supplier M decideswhether to label

Supplier M decideswhether to grant subsidy

and how much to subsidize

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decide whetherto invest in advertising and

how much to invest

Figure 7 Decision sequence of players in ASM

8 Complexity

Based on Equation (18) and cLlowastB α2B(144(1 minus tB)2) minus c0we have the following

tLlowastB 1 +

112

α2BK

minusK

c01113888 1113889

K 12c20α

2B +

144c40α4B + c30α6B1113969

1113874 1113875(13)

gt 0 (19)

cLlowastB

c0 3c0α2BK2 + K 12c20α2B minus K3( 1113857 minus c20α

2B α2B + 12K( 1113857( 1113857

K2 minus c0α2B( 11138572

(20)From Equation (18) and cLlowastB ge 0 we derive (3tLlowastB minus 1)

(2tLlowastB minus 1)le 0 as follows13le t

LlowastB le

12 (21)

First we analyze the optimal subsidy strategy of supplieraccording to Proposition 7 Longitudinally the subsidy formanufacturer B when supplier M chooses to label is higherthan that of the opposite Based on Proposition 4 manu-facturer B emerges with the ldquodiffusion of responsibilityrdquomindset in the face of the supplierrsquos decision to label+erefore supplier M will endowmanufacturer B with moresubsidies in an attempt to eliminate the mindset as much aspossible Horizontally when supplier M chooses to label thesubsidy to manufacturer B is higher than that to manu-facturer A because the supplier wants to improve his bar-gaining power in the negotiation with manufacturer A byclaiming to give more subsidies to manufacturer B

+en we analyze the optimal advertising investmentdecision of manufacturers When supplier chooses not tolabel the well-known manufacturer invests more than theweaker manufacturer to attract more attention from thesupplier +erefore the well-known manufacturer shouldalways retain its investment level to be higher than that of theweaker manufacturer to consolidate its market position Insummary supplier should endow the weaker manufacturerwith more subsidies when labeling and the well-knownmanufacturer should invest more than the weaker manu-facturer when supplier chooses not to label

Corollary 1 When supplier M chooses not to label anunderinvestment problem underlies the manufacturerrsquos ad-vertising investment In response subsidy can stimulate themanufacturersrsquo investment and mitigate the underinvestmentproblem

Proof By comparing the corresponding investment levels inTables 3 and 5 Corollary 1 can be proved For examplewhen supplier M chooses not to label manufacturer Arsquosoptimal investment levels in AIGM and ASM are (116)α2Aand (964)α2A as shown in Tables 3 and 5 respectively+erefore manufacturer Arsquos investment level in the AIGM isless than that in the ASM which reflects the un-derinvestment problem In addition subsidy can increasethe investment level of manufacturer A by (564)α2A

Corollary 1 confirms the existence of the un-derinvestment problem and shows that subsidy can stim-ulate manufacturersrsquo advertising investment level whichproves the importance of subsidy in coordinating the supplychain Finally we will further investigate the influence ofsubsidy on the supplier

Proposition 8 When the supplier chooses not to label thesubsidy strategy has a positive impact on the supplier suchthat the supplier will unconditionally issue subsidy to themanufacturers

Proof In the previous analysis we obtain the profits ofsupplier M when it does and does not grant subsidy If thesupplier chooses not to label then

πN3M minus πN2M

1576

9α2A + α2B1113872 1113873gt 0 (22)

We find that πN3M is always higher than πN2M which

indicates that the subsidy strategy has a positive impact onthe supplier who will unconditionally issue subsidy to themanufacturers when it opts not to label

In the ASM the advertising subsidy issued by thesupplier first promotes the investment of the manufacturersthat is the higher the investment the more improved thevalue of the products +is scenario thereby increases thebenefits of the cooperative alliance and ultimately improvesthe supplierrsquos profit+erefore the supplier should stimulatethe manufacturersrsquo investment by granting subsidies toincrease the intensity and promote the positive shift inequilibrium results of the competitive game so as to gainmore benefits in the next cooperative game In addition the

Supplier M

No label

Label

[PB + αBcB(12) ndash (1 + tB)cB PA + αAcA

(12) ndash (1 + tA)cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash (1 + tB)cB PA + αAcA(12) ndash c0 ndash (1 + tA)cA]

Figure 8 Income range of supplier in ASM

Table 5 Optimal decisions of players in ASM

SM clowastA clowastB tlowastA tlowastB

No label (964)α2A (164)α2B 13 13Label (964)α2A (α2B(144(1 minus tLlowastB )2)) minus c0 13 [13 12]

Complexity 9

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

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advertising investment game model which studies not onlythe labeling decision of the supplier but also the investmentdecision of manufacturers is established to determine theinfluences of advertising investment on the decisions ofplayers

Underinvestment may occur in advertising investmentbecause of the costs and risks Subsidy for investment costscan alleviate the underinvestment problem [12] +is studyintroduces an advertising subsidy mechanism wherethe supplier commits to pay a certain percentage of themanufacturersrsquo advertising investment In the non-cooperative stage the supplier decides on the subsidypercentage and whether or not to label the product In thecooperative stage surplus is divided according to theShapley value +e optimal subsidy percentage can beobtained via backward induction (Section 33) Manyscholars focused on the subsidy problem in supply chainsConsidering the investment problem of supply chainsProch et al [36] built a continuous time model and foundthat the supplier can encourage manufacturers to raise theirinvestment level by subsidizing a portion of their in-vestment costs to improve the underinvestment problemIn contrast to Proch et al [36] Alaei and Setak [37]proposed that subsidy negotiation can further improveadvertising performance by establishing and analyzing thedynamic differential game model In addition manyscholars proposed that subsidy is not confined to one-waysubsidy In certain conditions two-way subsidy is superiorto one-way subsidy For instance Song et al [23] in-troduced a two-way subsidy mechanism where the mem-bers of the supply chain can share investment costs withone another to coordinate the supply chain However theexisting literature on subsidy seldom considers manufac-turer heterogeneity As such we establish a tripartite gamemodel with advertising subsidy to study the optimal sub-sidy strategy of the supplier when faced with differentiatedmanufacturers and to alleviate underinvestment

+is study has the following key contributions to theexisting literature on competition and cooperation in or-ganic food supply chains First it provides optimal strategiesin labeling and advertising investment with consideration ofmanufacturer heterogeneity and consumer green preferenceIt presents interesting and unique explanations for severalphenomena Second it verifies the existence of un-derinvestment and introduces a further coordination pro-gram namely the advertising subsidy mechanism toalleviate the problem and achieve the Pareto improvement tocoordinate organic food supply chains Moreover it offersreasonable suggestions on the supplierrsquos subsidy andmanufacturersrsquo advertising investment In fact the optimaldecisions of enterprises will enhance their competitivenessin the highly competitive market [38]

+e remainder of this paper is structured as followsSection 2 presents the notations and assumptions Section 3describes and analyses the tripartite game model Section 4provides the numerical analysis Finally Section 5 concludesand summarizes the management insights and future di-rections of this study

2 Notations and Assumptions

First we provide several essential notations as follows

Pi highest price that consumers will pay for manu-facturer irsquos products where i isin AB

c0 labeling cost incurred by the supplierrsquos labelingstrategyci advertising cost incurred by manufacturer irsquos in-vestment in advertisement where i isin AB

αi investment return coefficient where i isin AB

πki profit of manufacturer i at the end of the co-operative stage where i isin AB and k takes values of 12 and 3 in the branded ingredient gamemodel (BIGM)advertising investment game model (AIGM) and ad-vertising subsidy mechanism (ASM) respectivelyπkM profit of the supplier at the end of the cooperativegame stage where k takes values of 1 2 and 3 in theBIGM AIGM and ASM respectivelyti supplierrsquos subsidy percentage for the manufacturerrsquosadvertising investment where i isin AB

Based on these notations we propose the followingassumptions to simplify the model

(1) +e production cost of the supplier is 0(2) Labeling cost is entirely borne by the supplier

whereas the advertising cost is entirely borne by themanufacturers

(3) +e sales volume is 1(4) Labeling does not affect the product of well-known

manufacturer A and increases the price of theproduct of manufacturer B by αBc

(12)0 [12] where

PB + αBc(12)0 ltPA

(5) Advertising and labeling are the same type of in-vestment that is for each manufacturer the in-vestment return coefficients of labeling andadvertising are equal which are expressed as αi andαA αB respectively

For convenience the definitions used in the followingsections are listed in the following paragraphs First weintroduce the meaning of certain symbols in the gameprocess In gamer set N 1 2 n each player j selectsstrategy sj isin Sj where Sj represents the strategy set ofplayer j Strategy vector (s1 sn) defines a utilitytransferable game and the corresponding characteristicfunction is defined as v(s1 sn) 2N⟶ R where 2N isthe power set of N In this study N MAB For any setC isin 2N v(s1 sn)(C) represents the revenue createdjointly by players in set C where v(s1 sn)(empty) 0 Onthis basis we set the following definitions accordingto [13]

Definition 1 In gamer set N a noncooperative game isdefined as (S1 Sn) whereas (N v) denotes cooperativegame +e biform game is defined as (S1 Sn N v)

Complexity 3

Definition 2 In cooperative game (N v) the Shapley valueof each player j is

ϕj(v) 1

|N|1113944

CsubN∖ j

|N| minus 1

|C|

⎛⎝ ⎞⎠

minus 1

(v(Ccup j1113864 1113865) minus v(C))

(1)

where |N| represents the number of all members in gamerset N |C| denotes the number of members in any subset C in

N and |N| minus 1|C|

1113888 1113889 refers to the number of combinations of

|C| elements taken from |N| minus 1 different elements

Definition 3 If any two alliances namely C1 and C2 satisfyC1 capC2 empty and

v C1 cupC2( 1113857ge v C1( 1113857 + v C2( 1113857 (2)

then the cooperative game (N v) is superadditive

3 Model Description and Analysis

+e tripartite game model proposed in this study consists ofthree parts namely BIGM AIGM and ASM which are usedto investigate the optimal strategy of labeling advertisinginvestment and subsidy respectively in organic food supplychains

First we establish the BIGM which only considers thelabeling decision of the supplier In this model the supplierrsquosstrategy set is SBIGMM Labeling No labeling +e AIGM isthen established to explore further the optimal decision of thesupplier regarding advertising investment and its impact thelabeling decision of the supplier and advertising investmentdecision of manufacturers +e AIGM involves the com-petitive game between manufacturers and cooperative gamebetween the supplier and manufacturers In this model thestrategy sets of the supplier and manufacturers areSAIGMM Labeling No labeling and SAIGMi Advertising Noadvertising respectively where i isin AB Finally to alleviateunderinvestment and coordinate the organic food supplychain we establish the ASM to elucidate further the influenceof subsidy In this context the strategy sets of the supplier andmanufacturers are SASMM Labeling No labelingtimes Sub-sidizing No subsidizing and SASMi Advertising No ad-vertising respectively

31 BIGM We assume that manufacturers A and B producethe same kind of organic food in the supply chain andsupplier M can supply raw materials to only one manu-facturer due to financial constraints Manufacturer A is awell-known manufacturer with rich experience in organicfood production whereas manufacturer B is an emergingfood manufacturer with relatively low reputation Con-sumers are willing to buy manufacturer Arsquos product at pricePA andmanufacturer Brsquos product at price PB where PB ltPAdue to the brand effect Figure 1 depicts the decision se-quence of the players in the BIGM

+e first stage is the noncooperative stage where sup-plier M decides whether or not to label the product asldquoorganic foodrdquo at cost c0 According to Assumption (4) inSection 2 labeling will bring investment returns αBc

(12)0 to

manufacturer B but no price premium to manufacturer Arsquosproduct as shown in Figure 2

+e optimal decision of supplier M is dependent on thecomparison and analysis of its expected profits under var-ious scenarios Figure 3 illustrates the income range ofsupplier M When supplier M opts not to label and to co-operate with manufacturer A the total revenue is PAwhereas manufacturer B gains zero benefit If supplier Mcooperates with manufacturer B then the total revenue is PBand PB＜PA +us the income range of supplier M in thiscase is [PB PA] Supplier M will prepay labeling cost c0 whenit decides to label the product If supplier M cooperates withmanufacturer A then the total revenue will be PA minus c0However if supplier M cooperates with manufacturer Bthen the total revenue will be PB + αBc

(12)0 minus c0 +erefore

the income range of supplier M in this case is [PB + αBc(12)0 minus

c0 PA minus c0]In the cooperative stage the supplier cooperates with

one manufacturer to produce and sell organic food andultimately gain profit At the end of the cooperative stage thesupply chain use the Shapley value method to divide profitNotably the manufacturerrsquos final profit is defined as πjwhere πj ϕj(v) j isin AB the final profit of supplier M isπM where πM ϕM(v) minus c0Γ We use indicator function Γ

1 if supplier M chooses to label and Γ 0 otherwise Byanalyzing the supplierrsquos final profit we can obtain its optimaldecision

Proposition 1 Only when the labeling cost is relatively lowwill the supplier choose to label Table 1 presents the supplierrsquosoptimal decision in the BIGM

Proof First we analyze the income range of supplier M Ifsupplier M opts not to label then the income range is[PB PA] otherwise the income range is [PB + αBc

(12)0 minus

c0 PA minus c0] Only when PB + αBc(12)0 minus c0 gtPB will supplier

M consider labeling that is

c0 lt α2B (3)

+en we use the Shapley value method to calculate thesupplierrsquos profit when choosing to label or not and use πL

1Mand πN

1M to express both decisions respectively as shown inTable 2 We find that when πN

1M lt πL1M namely

c0 lt136α2B (4)

supplier M will choose to label whereas it will not labelwhen c0 ge (136)α2B Notably the supplier decides not tolabel when the profits of labeling and no labeling are thesame

In addition after considering the price premium ofmanufacturer Brsquos product when labeling we also take theinequality in Assumption (4) in Section 2 into account as abasic condition for supplier Mrsquos decision to label namely

4 Complexity

c0 ltPA minus PB

αB1113888 1113889

2

(5)

When inequalities (3)ndash(5) are simultaneously metsupplier M will choose to label otherwise it will forgolabeling

Referring to Proposition 1 we find that the labelingdecision of the supplier is mainly dependent on labeling costwithout considering advertising investment +e suppliershould label to achieve higher profit given that labeling costis relatively low However when the labeling cost is high

labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofit At this point the supplier should choose not to label

According to Definition 3 we will verify whether co-operative game is superadditive as follows

Proposition 2 Cooperative game (N v) is superadditive

Proof In fact the manufacturer will not profit if it does nottake the supplierrsquos resource Hence we can infer thatv( i ) v( j1113864 1113865) 0 i j isin AB If supplier M cooperateswith manufacturer i then

v( M i ) v( M i j1113864 1113865)gt 0 (6)

hence v( j1113864 1113865) + v( M i )le v( M i j1113864 1113865) +us we derive thefollowing

v C1( 1113857 + v C2( 1113857le v C1 cupC2( 1113857 (7)

As a result cooperative game (N v) is superadditive

+e superadditivity of the cooperative game shows thatall players in the game are willing to cooperate because thetotal revenue from cooperation is always no less than thesum of the revenue from their respective operations +isnotion also proves the feasibility and rationality of themodel

In this subsection we dissect the supplierrsquos labelingdecision without considering the manufacturersrsquo advertisinginvestment and verify the superadditivity of the cooperativealliance Next we will establish the AIGM to further studythe investment decisions of the supplier and manufacturerswhen considering advertising investment

32 AIGM To increase competitiveness the manufacturerswill advertise their products On the basis of the BIGM weestablish the AIGM to further study the impact of adver-tising investment on the decision of supply chain membersWe assume that manufacturers A and B have the ability toadvertise their products Figure 4 shows the prices of themanufacturersrsquo products in the BIGM and AIGM

Supplier M decideswhether to label

Manufacturer goesinto production

Noncooperative stage Cooperative stage

Supplier and manufacturerdivide profit

Figure 1 Decision sequence of players in BIGM

Supplier MA B

0 0

0 0

No label

PA

PAPB + αBc0

(12)

PB

Label

A B

Figure 2 Prices of manufacturersrsquo product in BIGM

Supplier M

No label

Label

[PB PA]

[PB + αBc0(12) ndash c0 PA ndash c0]

Figure 3 Income range of supplier M in BIGM

Table 1 Supplierrsquos optimal decision in BIGM

Condition Decisionc0 lt (136)α2B and c0 lt ((PA minus PB)αB)2 Labelc0 ge (136)α2B No label

Table 2 Expected profit of supplier M in BIGM

SM π1MNo label πN1M (12)PA + (16)PBLabel πL1M (12)PA + (16)(PB + αBc

(12)0 ) minus c0

Complexity 5

In the noncooperative stage (S1 Sn) supplier Mdecides whether to label whereas manufacturers A and Bdecide whether to invest in advertising and how much toinvest In the cooperative stage (N v) the supplier andmanufacturers divide the profit Figure 5 illustrates thedecision sequence in the AIGM

In the analysis of the biform game (SA SB SM N v) weadopt the backwards induction which is contrary to thedecision order First profit set (πA πB πM) under strategyset (SA SB SM) is calculated using the Shapley valuemethod+en the optimal decision of the manufacturer onadvertising investment is obtained by analyzing theseprofits Finally we obtain the labeling decision of thesupplier

Figure 6 provides the income ranges of supplierM In thecase of manufacturers A and B investing in advertising ifsupplier M chooses not to label and cooperates withmanufacturer A then the total revenue is PA + αAc

(12)A minus cA

and manufacturer B gains no benefit However if supplier Mcooperates with manufacturer B then the total revenue isPB + αBc

(12)B minus cB +us the income range of supplier M in

this case is [PB + αBc(12)B minus cB PA + αAc

(12)A minus cA] If supplier

M chooses to label and cooperates with manufacturer Athen the total revenue will be PA + αAc

(12)A minus c0 minus cA If

supplier M cooperates with manufacturer B then the totalrevenue will be PB + αB(c0 + cB)(12) minus c0 minus cB In this casethe income range of supplier M is [PB + αB(c0 + cB)(12)minus

c0 minus cB PA + αAc(12)A minus c0 minus cA]

Notably however if one or both manufacturers do notinvest in advertising the supplierrsquos income range will be-come more complex Consequently we will analyze theinvestment decisions of the manufacturers

Proposition 3 Manufacturers A and B choose to invest inadvertising in AIGM

Proof When supplier M chooses not to label we can obtainthe profit of manufacturer B using the formula in Definition2 as follows

πN2B 16

PB + αBc(12)B1113872 1113873 minus cB (8)

Understanding that manufacturer Brsquos profit is only re-lated to its investment is easy that is advertising investmentcan bring positive net income to B +us manufacturer Bwill choose to invest in advertising +en we analyze Arsquosinvestment decision as follows

πN2A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus cA (9)

Under the premise that manufacturer B must invest inadvertising advertising investment can also bring positive netincome to manufacturer A who will also invest in advertisingat this moment +erefore manufacturers A and B will investin advertising when supplier M chooses not to label

Similarly when supplier M chooses to label we obtain

πL2B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cB

πL2A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cA

(10)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in AIGM

Proposition 3 indicates that both manufacturers shouldactively invest in advertising to strengthen competitivenessin the face of the existence of a competitor which equalsequilibrium in the dominant strategy by the competitivegame between two manufacturers Notably howeveroverinvestment may adversely affect manufacturers becauseexcessive investment will not only reduce the manufacturersrsquoshort-term operating capital but also damage profit and leadto bankruptcy +erefore manufacturers should furthermake a decision on the optimal levels of advertising in-vestment namely clowastA and clowastB In the following discussion wewill highlight each manufacturerrsquos optimal advertising in-vestment level under various strategies

Proposition 4 Table 3 presents the optimal amount of eachmanufacturerrsquo advertising investment

Proof We can obtain the manufacturersrsquo expected profitunder the different decisions of supplier M using the Shapleyvalue method When supplier M chooses not to label we canderive cNlowastA (116)α2A and cNlowastB (1144)α2B by calculatingdπN

2AdcA 0 and dπN2BdcB 0 respectively Similarlywhen M chooses to label we can obtain cLlowastA (116)α2A andcLlowastB (1144)α2B minus c0

Analysis of the manufacturersrsquo optimal advertising in-vestment level indicates that manufacturer heterogeneity can

A B

0 0

0 0

No label

Label0 0

0 0

No label

Label

A B

AIGM

BIGM

PA

PA

PB

PA + αAcA(12)

PA + αAcA(12)

PB + αB(c0 + cB)(12)

PB + αBcB(12)

PB + αBc0(12)

Figure 4 Prices of manufacturersrsquo products in BIGM and AIGM

6 Complexity

lead to differentiation of investment decisions +e supplierrsquosdecision to label has no effect onmanufacturer Arsquos investmentbut reduces manufacturer Brsquos investment According to As-sumption (4) in Section 2 labeling does not change the priceof manufacturer Arsquos products and will not thus affect man-ufacturer Arsquos decision However supplierMrsquos decision to labelwill increase the price of manufacturer Brsquos products whichindicates that the supplier partially undertakes the re-sponsibility that jointly improves the value of the products Inthis manner manufacturer Brsquos view that is ldquodiffusion ofresponsibilityrdquo is triggered and can be used to denote thepsyche of one who wants to decrease his responsibility at theexpense of the partnerrsquos efforts+erefore manufacturer Bwillreduce his investment level when supplier M chooses to labelHorizontally regardless of whether the supplier decides tolabels or not the well-known manufacturer will always investmore in advertising compared with the weaker manufacturerbecause the well-known manufacturer wants to consolidatecompetitiveness and attractsmore attention from the supplierIn summary the weaker manufacturer should appropriatelyreduce its investment in advertising when the supplier choosesto label whereas the well-known manufacturer should retainits investment level to be always higher than that of the weakermanufacturer to solidify its market position andcompetitiveness

We will further discuss the supplierrsquos decision to label inthe face of the manufacturersrsquo equilibrium strategies

Proposition 5 Considering advertising investment supplierM always chooses not to label

Proof According to Table 4 we find that πN2M minus πL

2M c0 gt 0+erefore supplier M who pursues maximum profit alwaysopts not to label

From the perspective of the individual interests of de-cision makers and in the face of the manufacturersrsquo in-vestment efforts the supplier will generate the ldquodiffusion ofresponsibilityrdquo mindset and choose not to label to minimizeits investment From the perspective of the overall interest ofthe supply chain when the manufacturers contribute to thecooperative alliance through advertising investment thesupplierrsquos active investment behavior that it still chooses tolabel may let the total investment outweigh the total returnand enter the stage of diminishing returns on scale Intheory the competitive game equilibrium result that allmanufacturers invest in advertising improves the supplierrsquosadvantage in the cooperative game which leads to the co-operative game equilibrium result where the supplier doesnot need to label

In this subsection we set up the AIGM and use theShapley value method to calculate the profit of each playerunder different scenarios and finally obtain optimal de-cisions by backwards induction Finding shows that in thetripartite game with advertising investment between onesupplier and two heterogeneous manufacturers the lattershould invest in advertising to enhance competitivenessand the possibility of cooperation with the supplier Doingso will contribute to improving the value of products suchthat the supplier does not need to label In the followingsubsection we will verify the existence of the un-derinvestment problem and further shed light on theoptimal decisions of the supplier and manufacturers inASM

33 ASM +e supplier usually gives the manufacturers anincentive policy to stimulate investment In this subsectionwe introduce the advertising subsidy mechanism where thesupplier will commit to pay a certain percentage of themanufacturersrsquo advertising investment Figure 7 providesthe decision sequence in ASM

For ease of distinction we denote π2j and π3j to rep-resent the profit of j in the AIGM and ASM respectivelywhere j isin MAB ti refers to the supplierrsquos subsidy per-centage for the manufacturerrsquos advertising investment

Supplier M decideswhether to label

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decidewhether to investin advertising and

how much to invest

Figure 5 Decision sequence of players in AIGM

Supplier M

No label

Label

[PB + αBcB(12) ndash cB PA + αAcA

(12) ndash cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash cB PA + αAcA(12) ndash c0 ndash cA]

Figure 6 Income ranges of supplier M in AIGM

Table 3 Optimal amount of advertising investment

SM clowastA clowastB

No label (116)α2A (1144)α2BLabel (116)α2A (1144)α2B minus c0

Table 4 Expected benefits of supplier M in AIGM

SM π2MNo label πN2M (12)PA + (16)PB + (18)α2A + (172)α2BLabel πL2M (12)PA + (16)PB + (18)α2A + (172)α2B minus c0

Complexity 7

+erefore we can express the advertising subsidy mecha-nism as follows

π3A π2A + tAcA

π3B π2B + tBcB

π3M π2M minus tAcA minus tBcB

(11)

Considering the effect of subsidy on earnings based onthe AIGM we obtain the income range of the supplier inASM as shown in Figure 8

Using the same method of analysis in the AIGM weobtain the optimum decisions of the supplier and manu-facturers First we analyze whether the manufacturers willchoose to invest in advertising in ASM

Proposition 6 Manufacturers A and B choose to invest inadvertising in ASM

Proof When supplier M chooses not to label manufacturerBrsquos profits can be acquired by the Shapley value method asfollows

πN3B

16

PB + αBc(12)B1113872 1113873 minus 1 minus tB( 1113857cB (12)

Finding that manufacturer Brsquos profit is only related to itsinvestment and advertising investment can bring a positivenet income to manufacturer B is easy to understand +usmanufacturer B will choose to invest in advertising+en weanalyze manufacturer Arsquos investment decision and derive itsprofit as follows

πN3A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus 1 minus tA( 1113857cA

(13)

Under the premise that manufacturer B must invest inadvertising manufacturer A can derive positive net incomefrom advertising investment+erefore manufacturer A willalso invest in advertising

Similarly when supplier M chooses to label we have

πL3B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus 1 minus tB( 1113857cB (14)

πL3A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus 1 minus tA( 1113857cA

(15)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in ASM

We find that under the advertising subsidy mechanismthe manufacturers will still choose to invest in advertising Inaddition we can speculate that the manufacturers are morewilling to invest because the subsidy is harmless and ben-eficial to them +erefore the manufacturers may increaseinvestment under the advertising subsidy mechanism Nextwe will verify whether subsidy will promote the manufac-turersrsquo investment by analyzing the manufacturersrsquo optimalinvestment level and elucidate the optimal subsidy strategy

Proposition 7 Table 5 presents the optimal decisions ofplayers in ASM

Proof We can obtain the profit functions of the supplierunder different circumstances using the Shapley valuemethod When the supplier chooses not to label then

πN3M

12

PA + αAc(12)A1113872 1113873 +

16

PB + αBc(12)B1113872 1113873 minus tAcA minus tBcB

(16)

Otherwise

πL3M 12

PA + αAc(12)A1113872 1113873 +

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus tAcA minus tBcB minus c0

(17)

Based on equations (12)ndash(17) we can obtain the optimaldecisions of advertising investment and subsidy When Mchooses not to label we can derive cNlowastA α2A(16(1 minus tA)2)

and cNlowastB α2B(144(1 minus tB)2) from dπN3AdcA 0 and fromdπN

3BdcB 0 respectively +en we can obtain tNlowastA 13and tNlowastB 13 from zπN3MztA 0 and from zπN

3MztB 0respectively +erefore we have cNlowastA (964)α2A andcNlowastB (164)α2B

When supplier M opts to label we can derive cLlowastA

α2A(16(1 minus tA)2) and cLlowastB α2B(144(1 minus tB)2) minus c0 fromdπL

3AdcA 0 and from dπL3BdcB 0 respectively +en wehave tLlowastA 13 from zπL

3MztA 0 Based on zπL3MztB 0

we find that tLlowastB satisfies

α2B 1 minus 3tB( 1113857 + 144c0 1 minus tB( 11138573

0 (18)

Supplier M decideswhether to label

Supplier M decideswhether to grant subsidy

and how much to subsidize

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decide whetherto invest in advertising and

how much to invest

Figure 7 Decision sequence of players in ASM

8 Complexity

Based on Equation (18) and cLlowastB α2B(144(1 minus tB)2) minus c0we have the following

tLlowastB 1 +

112

α2BK

minusK

c01113888 1113889

K 12c20α

2B +

144c40α4B + c30α6B1113969

1113874 1113875(13)

gt 0 (19)

cLlowastB

c0 3c0α2BK2 + K 12c20α2B minus K3( 1113857 minus c20α

2B α2B + 12K( 1113857( 1113857

K2 minus c0α2B( 11138572

(20)From Equation (18) and cLlowastB ge 0 we derive (3tLlowastB minus 1)

(2tLlowastB minus 1)le 0 as follows13le t

LlowastB le

12 (21)

First we analyze the optimal subsidy strategy of supplieraccording to Proposition 7 Longitudinally the subsidy formanufacturer B when supplier M chooses to label is higherthan that of the opposite Based on Proposition 4 manu-facturer B emerges with the ldquodiffusion of responsibilityrdquomindset in the face of the supplierrsquos decision to label+erefore supplier M will endowmanufacturer B with moresubsidies in an attempt to eliminate the mindset as much aspossible Horizontally when supplier M chooses to label thesubsidy to manufacturer B is higher than that to manu-facturer A because the supplier wants to improve his bar-gaining power in the negotiation with manufacturer A byclaiming to give more subsidies to manufacturer B

+en we analyze the optimal advertising investmentdecision of manufacturers When supplier chooses not tolabel the well-known manufacturer invests more than theweaker manufacturer to attract more attention from thesupplier +erefore the well-known manufacturer shouldalways retain its investment level to be higher than that of theweaker manufacturer to consolidate its market position Insummary supplier should endow the weaker manufacturerwith more subsidies when labeling and the well-knownmanufacturer should invest more than the weaker manu-facturer when supplier chooses not to label

Corollary 1 When supplier M chooses not to label anunderinvestment problem underlies the manufacturerrsquos ad-vertising investment In response subsidy can stimulate themanufacturersrsquo investment and mitigate the underinvestmentproblem

Proof By comparing the corresponding investment levels inTables 3 and 5 Corollary 1 can be proved For examplewhen supplier M chooses not to label manufacturer Arsquosoptimal investment levels in AIGM and ASM are (116)α2Aand (964)α2A as shown in Tables 3 and 5 respectively+erefore manufacturer Arsquos investment level in the AIGM isless than that in the ASM which reflects the un-derinvestment problem In addition subsidy can increasethe investment level of manufacturer A by (564)α2A

Corollary 1 confirms the existence of the un-derinvestment problem and shows that subsidy can stim-ulate manufacturersrsquo advertising investment level whichproves the importance of subsidy in coordinating the supplychain Finally we will further investigate the influence ofsubsidy on the supplier

Proposition 8 When the supplier chooses not to label thesubsidy strategy has a positive impact on the supplier suchthat the supplier will unconditionally issue subsidy to themanufacturers

Proof In the previous analysis we obtain the profits ofsupplier M when it does and does not grant subsidy If thesupplier chooses not to label then

πN3M minus πN2M

1576

9α2A + α2B1113872 1113873gt 0 (22)

We find that πN3M is always higher than πN2M which

indicates that the subsidy strategy has a positive impact onthe supplier who will unconditionally issue subsidy to themanufacturers when it opts not to label

In the ASM the advertising subsidy issued by thesupplier first promotes the investment of the manufacturersthat is the higher the investment the more improved thevalue of the products +is scenario thereby increases thebenefits of the cooperative alliance and ultimately improvesthe supplierrsquos profit+erefore the supplier should stimulatethe manufacturersrsquo investment by granting subsidies toincrease the intensity and promote the positive shift inequilibrium results of the competitive game so as to gainmore benefits in the next cooperative game In addition the

Supplier M

No label

Label

[PB + αBcB(12) ndash (1 + tB)cB PA + αAcA

(12) ndash (1 + tA)cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash (1 + tB)cB PA + αAcA(12) ndash c0 ndash (1 + tA)cA]

Figure 8 Income range of supplier in ASM

Table 5 Optimal decisions of players in ASM

SM clowastA clowastB tlowastA tlowastB

No label (964)α2A (164)α2B 13 13Label (964)α2A (α2B(144(1 minus tLlowastB )2)) minus c0 13 [13 12]

Complexity 9

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

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MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

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Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

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Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Definition 2 In cooperative game (N v) the Shapley valueof each player j is

ϕj(v) 1

|N|1113944

CsubN∖ j

|N| minus 1

|C|

⎛⎝ ⎞⎠

minus 1

(v(Ccup j1113864 1113865) minus v(C))

(1)

where |N| represents the number of all members in gamerset N |C| denotes the number of members in any subset C in

N and |N| minus 1|C|

1113888 1113889 refers to the number of combinations of

|C| elements taken from |N| minus 1 different elements

Definition 3 If any two alliances namely C1 and C2 satisfyC1 capC2 empty and

v C1 cupC2( 1113857ge v C1( 1113857 + v C2( 1113857 (2)

then the cooperative game (N v) is superadditive

3 Model Description and Analysis

+e tripartite game model proposed in this study consists ofthree parts namely BIGM AIGM and ASM which are usedto investigate the optimal strategy of labeling advertisinginvestment and subsidy respectively in organic food supplychains

First we establish the BIGM which only considers thelabeling decision of the supplier In this model the supplierrsquosstrategy set is SBIGMM Labeling No labeling +e AIGM isthen established to explore further the optimal decision of thesupplier regarding advertising investment and its impact thelabeling decision of the supplier and advertising investmentdecision of manufacturers +e AIGM involves the com-petitive game between manufacturers and cooperative gamebetween the supplier and manufacturers In this model thestrategy sets of the supplier and manufacturers areSAIGMM Labeling No labeling and SAIGMi Advertising Noadvertising respectively where i isin AB Finally to alleviateunderinvestment and coordinate the organic food supplychain we establish the ASM to elucidate further the influenceof subsidy In this context the strategy sets of the supplier andmanufacturers are SASMM Labeling No labelingtimes Sub-sidizing No subsidizing and SASMi Advertising No ad-vertising respectively

31 BIGM We assume that manufacturers A and B producethe same kind of organic food in the supply chain andsupplier M can supply raw materials to only one manu-facturer due to financial constraints Manufacturer A is awell-known manufacturer with rich experience in organicfood production whereas manufacturer B is an emergingfood manufacturer with relatively low reputation Con-sumers are willing to buy manufacturer Arsquos product at pricePA andmanufacturer Brsquos product at price PB where PB ltPAdue to the brand effect Figure 1 depicts the decision se-quence of the players in the BIGM

+e first stage is the noncooperative stage where sup-plier M decides whether or not to label the product asldquoorganic foodrdquo at cost c0 According to Assumption (4) inSection 2 labeling will bring investment returns αBc

(12)0 to

manufacturer B but no price premium to manufacturer Arsquosproduct as shown in Figure 2

+e optimal decision of supplier M is dependent on thecomparison and analysis of its expected profits under var-ious scenarios Figure 3 illustrates the income range ofsupplier M When supplier M opts not to label and to co-operate with manufacturer A the total revenue is PAwhereas manufacturer B gains zero benefit If supplier Mcooperates with manufacturer B then the total revenue is PBand PB＜PA +us the income range of supplier M in thiscase is [PB PA] Supplier M will prepay labeling cost c0 whenit decides to label the product If supplier M cooperates withmanufacturer A then the total revenue will be PA minus c0However if supplier M cooperates with manufacturer Bthen the total revenue will be PB + αBc

(12)0 minus c0 +erefore

the income range of supplier M in this case is [PB + αBc(12)0 minus

c0 PA minus c0]In the cooperative stage the supplier cooperates with

one manufacturer to produce and sell organic food andultimately gain profit At the end of the cooperative stage thesupply chain use the Shapley value method to divide profitNotably the manufacturerrsquos final profit is defined as πjwhere πj ϕj(v) j isin AB the final profit of supplier M isπM where πM ϕM(v) minus c0Γ We use indicator function Γ

1 if supplier M chooses to label and Γ 0 otherwise Byanalyzing the supplierrsquos final profit we can obtain its optimaldecision

Proposition 1 Only when the labeling cost is relatively lowwill the supplier choose to label Table 1 presents the supplierrsquosoptimal decision in the BIGM

Proof First we analyze the income range of supplier M Ifsupplier M opts not to label then the income range is[PB PA] otherwise the income range is [PB + αBc

(12)0 minus

c0 PA minus c0] Only when PB + αBc(12)0 minus c0 gtPB will supplier

M consider labeling that is

c0 lt α2B (3)

+en we use the Shapley value method to calculate thesupplierrsquos profit when choosing to label or not and use πL

1Mand πN

1M to express both decisions respectively as shown inTable 2 We find that when πN

1M lt πL1M namely

c0 lt136α2B (4)

supplier M will choose to label whereas it will not labelwhen c0 ge (136)α2B Notably the supplier decides not tolabel when the profits of labeling and no labeling are thesame

In addition after considering the price premium ofmanufacturer Brsquos product when labeling we also take theinequality in Assumption (4) in Section 2 into account as abasic condition for supplier Mrsquos decision to label namely

4 Complexity

c0 ltPA minus PB

αB1113888 1113889

2

(5)

When inequalities (3)ndash(5) are simultaneously metsupplier M will choose to label otherwise it will forgolabeling

Referring to Proposition 1 we find that the labelingdecision of the supplier is mainly dependent on labeling costwithout considering advertising investment +e suppliershould label to achieve higher profit given that labeling costis relatively low However when the labeling cost is high

labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofit At this point the supplier should choose not to label

According to Definition 3 we will verify whether co-operative game is superadditive as follows

Proposition 2 Cooperative game (N v) is superadditive

Proof In fact the manufacturer will not profit if it does nottake the supplierrsquos resource Hence we can infer thatv( i ) v( j1113864 1113865) 0 i j isin AB If supplier M cooperateswith manufacturer i then

v( M i ) v( M i j1113864 1113865)gt 0 (6)

hence v( j1113864 1113865) + v( M i )le v( M i j1113864 1113865) +us we derive thefollowing

v C1( 1113857 + v C2( 1113857le v C1 cupC2( 1113857 (7)

As a result cooperative game (N v) is superadditive

+e superadditivity of the cooperative game shows thatall players in the game are willing to cooperate because thetotal revenue from cooperation is always no less than thesum of the revenue from their respective operations +isnotion also proves the feasibility and rationality of themodel

In this subsection we dissect the supplierrsquos labelingdecision without considering the manufacturersrsquo advertisinginvestment and verify the superadditivity of the cooperativealliance Next we will establish the AIGM to further studythe investment decisions of the supplier and manufacturerswhen considering advertising investment

32 AIGM To increase competitiveness the manufacturerswill advertise their products On the basis of the BIGM weestablish the AIGM to further study the impact of adver-tising investment on the decision of supply chain membersWe assume that manufacturers A and B have the ability toadvertise their products Figure 4 shows the prices of themanufacturersrsquo products in the BIGM and AIGM

Supplier M decideswhether to label

Manufacturer goesinto production

Noncooperative stage Cooperative stage

Supplier and manufacturerdivide profit

Figure 1 Decision sequence of players in BIGM

Supplier MA B

0 0

0 0

No label

PA

PAPB + αBc0

(12)

PB

Label

A B

Figure 2 Prices of manufacturersrsquo product in BIGM

Supplier M

No label

Label

[PB PA]

[PB + αBc0(12) ndash c0 PA ndash c0]

Figure 3 Income range of supplier M in BIGM

Table 1 Supplierrsquos optimal decision in BIGM

Condition Decisionc0 lt (136)α2B and c0 lt ((PA minus PB)αB)2 Labelc0 ge (136)α2B No label

Table 2 Expected profit of supplier M in BIGM

SM π1MNo label πN1M (12)PA + (16)PBLabel πL1M (12)PA + (16)(PB + αBc

(12)0 ) minus c0

Complexity 5

In the noncooperative stage (S1 Sn) supplier Mdecides whether to label whereas manufacturers A and Bdecide whether to invest in advertising and how much toinvest In the cooperative stage (N v) the supplier andmanufacturers divide the profit Figure 5 illustrates thedecision sequence in the AIGM

In the analysis of the biform game (SA SB SM N v) weadopt the backwards induction which is contrary to thedecision order First profit set (πA πB πM) under strategyset (SA SB SM) is calculated using the Shapley valuemethod+en the optimal decision of the manufacturer onadvertising investment is obtained by analyzing theseprofits Finally we obtain the labeling decision of thesupplier

Figure 6 provides the income ranges of supplierM In thecase of manufacturers A and B investing in advertising ifsupplier M chooses not to label and cooperates withmanufacturer A then the total revenue is PA + αAc

(12)A minus cA

and manufacturer B gains no benefit However if supplier Mcooperates with manufacturer B then the total revenue isPB + αBc

(12)B minus cB +us the income range of supplier M in

this case is [PB + αBc(12)B minus cB PA + αAc

(12)A minus cA] If supplier

M chooses to label and cooperates with manufacturer Athen the total revenue will be PA + αAc

(12)A minus c0 minus cA If

supplier M cooperates with manufacturer B then the totalrevenue will be PB + αB(c0 + cB)(12) minus c0 minus cB In this casethe income range of supplier M is [PB + αB(c0 + cB)(12)minus

c0 minus cB PA + αAc(12)A minus c0 minus cA]

Notably however if one or both manufacturers do notinvest in advertising the supplierrsquos income range will be-come more complex Consequently we will analyze theinvestment decisions of the manufacturers

Proposition 3 Manufacturers A and B choose to invest inadvertising in AIGM

Proof When supplier M chooses not to label we can obtainthe profit of manufacturer B using the formula in Definition2 as follows

πN2B 16

PB + αBc(12)B1113872 1113873 minus cB (8)

Understanding that manufacturer Brsquos profit is only re-lated to its investment is easy that is advertising investmentcan bring positive net income to B +us manufacturer Bwill choose to invest in advertising +en we analyze Arsquosinvestment decision as follows

πN2A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus cA (9)

Under the premise that manufacturer B must invest inadvertising advertising investment can also bring positive netincome to manufacturer A who will also invest in advertisingat this moment +erefore manufacturers A and B will investin advertising when supplier M chooses not to label

Similarly when supplier M chooses to label we obtain

πL2B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cB

πL2A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cA

(10)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in AIGM

Proposition 3 indicates that both manufacturers shouldactively invest in advertising to strengthen competitivenessin the face of the existence of a competitor which equalsequilibrium in the dominant strategy by the competitivegame between two manufacturers Notably howeveroverinvestment may adversely affect manufacturers becauseexcessive investment will not only reduce the manufacturersrsquoshort-term operating capital but also damage profit and leadto bankruptcy +erefore manufacturers should furthermake a decision on the optimal levels of advertising in-vestment namely clowastA and clowastB In the following discussion wewill highlight each manufacturerrsquos optimal advertising in-vestment level under various strategies

Proposition 4 Table 3 presents the optimal amount of eachmanufacturerrsquo advertising investment

Proof We can obtain the manufacturersrsquo expected profitunder the different decisions of supplier M using the Shapleyvalue method When supplier M chooses not to label we canderive cNlowastA (116)α2A and cNlowastB (1144)α2B by calculatingdπN

2AdcA 0 and dπN2BdcB 0 respectively Similarlywhen M chooses to label we can obtain cLlowastA (116)α2A andcLlowastB (1144)α2B minus c0

Analysis of the manufacturersrsquo optimal advertising in-vestment level indicates that manufacturer heterogeneity can

A B

0 0

0 0

No label

Label0 0

0 0

No label

Label

A B

AIGM

BIGM

PA

PA

PB

PA + αAcA(12)

PA + αAcA(12)

PB + αB(c0 + cB)(12)

PB + αBcB(12)

PB + αBc0(12)

Figure 4 Prices of manufacturersrsquo products in BIGM and AIGM

6 Complexity

lead to differentiation of investment decisions +e supplierrsquosdecision to label has no effect onmanufacturer Arsquos investmentbut reduces manufacturer Brsquos investment According to As-sumption (4) in Section 2 labeling does not change the priceof manufacturer Arsquos products and will not thus affect man-ufacturer Arsquos decision However supplierMrsquos decision to labelwill increase the price of manufacturer Brsquos products whichindicates that the supplier partially undertakes the re-sponsibility that jointly improves the value of the products Inthis manner manufacturer Brsquos view that is ldquodiffusion ofresponsibilityrdquo is triggered and can be used to denote thepsyche of one who wants to decrease his responsibility at theexpense of the partnerrsquos efforts+erefore manufacturer Bwillreduce his investment level when supplier M chooses to labelHorizontally regardless of whether the supplier decides tolabels or not the well-known manufacturer will always investmore in advertising compared with the weaker manufacturerbecause the well-known manufacturer wants to consolidatecompetitiveness and attractsmore attention from the supplierIn summary the weaker manufacturer should appropriatelyreduce its investment in advertising when the supplier choosesto label whereas the well-known manufacturer should retainits investment level to be always higher than that of the weakermanufacturer to solidify its market position andcompetitiveness

We will further discuss the supplierrsquos decision to label inthe face of the manufacturersrsquo equilibrium strategies

Proposition 5 Considering advertising investment supplierM always chooses not to label

Proof According to Table 4 we find that πN2M minus πL

2M c0 gt 0+erefore supplier M who pursues maximum profit alwaysopts not to label

From the perspective of the individual interests of de-cision makers and in the face of the manufacturersrsquo in-vestment efforts the supplier will generate the ldquodiffusion ofresponsibilityrdquo mindset and choose not to label to minimizeits investment From the perspective of the overall interest ofthe supply chain when the manufacturers contribute to thecooperative alliance through advertising investment thesupplierrsquos active investment behavior that it still chooses tolabel may let the total investment outweigh the total returnand enter the stage of diminishing returns on scale Intheory the competitive game equilibrium result that allmanufacturers invest in advertising improves the supplierrsquosadvantage in the cooperative game which leads to the co-operative game equilibrium result where the supplier doesnot need to label

In this subsection we set up the AIGM and use theShapley value method to calculate the profit of each playerunder different scenarios and finally obtain optimal de-cisions by backwards induction Finding shows that in thetripartite game with advertising investment between onesupplier and two heterogeneous manufacturers the lattershould invest in advertising to enhance competitivenessand the possibility of cooperation with the supplier Doingso will contribute to improving the value of products suchthat the supplier does not need to label In the followingsubsection we will verify the existence of the un-derinvestment problem and further shed light on theoptimal decisions of the supplier and manufacturers inASM

33 ASM +e supplier usually gives the manufacturers anincentive policy to stimulate investment In this subsectionwe introduce the advertising subsidy mechanism where thesupplier will commit to pay a certain percentage of themanufacturersrsquo advertising investment Figure 7 providesthe decision sequence in ASM

For ease of distinction we denote π2j and π3j to rep-resent the profit of j in the AIGM and ASM respectivelywhere j isin MAB ti refers to the supplierrsquos subsidy per-centage for the manufacturerrsquos advertising investment

Supplier M decideswhether to label

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decidewhether to investin advertising and

how much to invest

Figure 5 Decision sequence of players in AIGM

Supplier M

No label

Label

[PB + αBcB(12) ndash cB PA + αAcA

(12) ndash cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash cB PA + αAcA(12) ndash c0 ndash cA]

Figure 6 Income ranges of supplier M in AIGM

Table 3 Optimal amount of advertising investment

SM clowastA clowastB

No label (116)α2A (1144)α2BLabel (116)α2A (1144)α2B minus c0

Table 4 Expected benefits of supplier M in AIGM

SM π2MNo label πN2M (12)PA + (16)PB + (18)α2A + (172)α2BLabel πL2M (12)PA + (16)PB + (18)α2A + (172)α2B minus c0

Complexity 7

+erefore we can express the advertising subsidy mecha-nism as follows

π3A π2A + tAcA

π3B π2B + tBcB

π3M π2M minus tAcA minus tBcB

(11)

Considering the effect of subsidy on earnings based onthe AIGM we obtain the income range of the supplier inASM as shown in Figure 8

Using the same method of analysis in the AIGM weobtain the optimum decisions of the supplier and manu-facturers First we analyze whether the manufacturers willchoose to invest in advertising in ASM

Proposition 6 Manufacturers A and B choose to invest inadvertising in ASM

Proof When supplier M chooses not to label manufacturerBrsquos profits can be acquired by the Shapley value method asfollows

πN3B

16

PB + αBc(12)B1113872 1113873 minus 1 minus tB( 1113857cB (12)

Finding that manufacturer Brsquos profit is only related to itsinvestment and advertising investment can bring a positivenet income to manufacturer B is easy to understand +usmanufacturer B will choose to invest in advertising+en weanalyze manufacturer Arsquos investment decision and derive itsprofit as follows

πN3A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus 1 minus tA( 1113857cA

(13)

Under the premise that manufacturer B must invest inadvertising manufacturer A can derive positive net incomefrom advertising investment+erefore manufacturer A willalso invest in advertising

Similarly when supplier M chooses to label we have

πL3B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus 1 minus tB( 1113857cB (14)

πL3A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus 1 minus tA( 1113857cA

(15)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in ASM

We find that under the advertising subsidy mechanismthe manufacturers will still choose to invest in advertising Inaddition we can speculate that the manufacturers are morewilling to invest because the subsidy is harmless and ben-eficial to them +erefore the manufacturers may increaseinvestment under the advertising subsidy mechanism Nextwe will verify whether subsidy will promote the manufac-turersrsquo investment by analyzing the manufacturersrsquo optimalinvestment level and elucidate the optimal subsidy strategy

Proposition 7 Table 5 presents the optimal decisions ofplayers in ASM

Proof We can obtain the profit functions of the supplierunder different circumstances using the Shapley valuemethod When the supplier chooses not to label then

πN3M

12

PA + αAc(12)A1113872 1113873 +

16

PB + αBc(12)B1113872 1113873 minus tAcA minus tBcB

(16)

Otherwise

πL3M 12

PA + αAc(12)A1113872 1113873 +

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus tAcA minus tBcB minus c0

(17)

Based on equations (12)ndash(17) we can obtain the optimaldecisions of advertising investment and subsidy When Mchooses not to label we can derive cNlowastA α2A(16(1 minus tA)2)

and cNlowastB α2B(144(1 minus tB)2) from dπN3AdcA 0 and fromdπN

3BdcB 0 respectively +en we can obtain tNlowastA 13and tNlowastB 13 from zπN3MztA 0 and from zπN

3MztB 0respectively +erefore we have cNlowastA (964)α2A andcNlowastB (164)α2B

When supplier M opts to label we can derive cLlowastA

α2A(16(1 minus tA)2) and cLlowastB α2B(144(1 minus tB)2) minus c0 fromdπL

3AdcA 0 and from dπL3BdcB 0 respectively +en wehave tLlowastA 13 from zπL

3MztA 0 Based on zπL3MztB 0

we find that tLlowastB satisfies

α2B 1 minus 3tB( 1113857 + 144c0 1 minus tB( 11138573

0 (18)

Supplier M decideswhether to label

Supplier M decideswhether to grant subsidy

and how much to subsidize

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decide whetherto invest in advertising and

how much to invest

Figure 7 Decision sequence of players in ASM

8 Complexity

Based on Equation (18) and cLlowastB α2B(144(1 minus tB)2) minus c0we have the following

tLlowastB 1 +

112

α2BK

minusK

c01113888 1113889

K 12c20α

2B +

144c40α4B + c30α6B1113969

1113874 1113875(13)

gt 0 (19)

cLlowastB

c0 3c0α2BK2 + K 12c20α2B minus K3( 1113857 minus c20α

2B α2B + 12K( 1113857( 1113857

K2 minus c0α2B( 11138572

(20)From Equation (18) and cLlowastB ge 0 we derive (3tLlowastB minus 1)

(2tLlowastB minus 1)le 0 as follows13le t

LlowastB le

12 (21)

First we analyze the optimal subsidy strategy of supplieraccording to Proposition 7 Longitudinally the subsidy formanufacturer B when supplier M chooses to label is higherthan that of the opposite Based on Proposition 4 manu-facturer B emerges with the ldquodiffusion of responsibilityrdquomindset in the face of the supplierrsquos decision to label+erefore supplier M will endowmanufacturer B with moresubsidies in an attempt to eliminate the mindset as much aspossible Horizontally when supplier M chooses to label thesubsidy to manufacturer B is higher than that to manu-facturer A because the supplier wants to improve his bar-gaining power in the negotiation with manufacturer A byclaiming to give more subsidies to manufacturer B

+en we analyze the optimal advertising investmentdecision of manufacturers When supplier chooses not tolabel the well-known manufacturer invests more than theweaker manufacturer to attract more attention from thesupplier +erefore the well-known manufacturer shouldalways retain its investment level to be higher than that of theweaker manufacturer to consolidate its market position Insummary supplier should endow the weaker manufacturerwith more subsidies when labeling and the well-knownmanufacturer should invest more than the weaker manu-facturer when supplier chooses not to label

Corollary 1 When supplier M chooses not to label anunderinvestment problem underlies the manufacturerrsquos ad-vertising investment In response subsidy can stimulate themanufacturersrsquo investment and mitigate the underinvestmentproblem

Proof By comparing the corresponding investment levels inTables 3 and 5 Corollary 1 can be proved For examplewhen supplier M chooses not to label manufacturer Arsquosoptimal investment levels in AIGM and ASM are (116)α2Aand (964)α2A as shown in Tables 3 and 5 respectively+erefore manufacturer Arsquos investment level in the AIGM isless than that in the ASM which reflects the un-derinvestment problem In addition subsidy can increasethe investment level of manufacturer A by (564)α2A

Corollary 1 confirms the existence of the un-derinvestment problem and shows that subsidy can stim-ulate manufacturersrsquo advertising investment level whichproves the importance of subsidy in coordinating the supplychain Finally we will further investigate the influence ofsubsidy on the supplier

Proposition 8 When the supplier chooses not to label thesubsidy strategy has a positive impact on the supplier suchthat the supplier will unconditionally issue subsidy to themanufacturers

Proof In the previous analysis we obtain the profits ofsupplier M when it does and does not grant subsidy If thesupplier chooses not to label then

πN3M minus πN2M

1576

9α2A + α2B1113872 1113873gt 0 (22)

We find that πN3M is always higher than πN2M which

indicates that the subsidy strategy has a positive impact onthe supplier who will unconditionally issue subsidy to themanufacturers when it opts not to label

In the ASM the advertising subsidy issued by thesupplier first promotes the investment of the manufacturersthat is the higher the investment the more improved thevalue of the products +is scenario thereby increases thebenefits of the cooperative alliance and ultimately improvesthe supplierrsquos profit+erefore the supplier should stimulatethe manufacturersrsquo investment by granting subsidies toincrease the intensity and promote the positive shift inequilibrium results of the competitive game so as to gainmore benefits in the next cooperative game In addition the

Supplier M

No label

Label

[PB + αBcB(12) ndash (1 + tB)cB PA + αAcA

(12) ndash (1 + tA)cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash (1 + tB)cB PA + αAcA(12) ndash c0 ndash (1 + tA)cA]

Figure 8 Income range of supplier in ASM

Table 5 Optimal decisions of players in ASM

SM clowastA clowastB tlowastA tlowastB

No label (964)α2A (164)α2B 13 13Label (964)α2A (α2B(144(1 minus tLlowastB )2)) minus c0 13 [13 12]

Complexity 9

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

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Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

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Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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AnalysisInternational Journal of

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

c0 ltPA minus PB

αB1113888 1113889

2

(5)

When inequalities (3)ndash(5) are simultaneously metsupplier M will choose to label otherwise it will forgolabeling

Referring to Proposition 1 we find that the labelingdecision of the supplier is mainly dependent on labeling costwithout considering advertising investment +e suppliershould label to achieve higher profit given that labeling costis relatively low However when the labeling cost is high

labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofit At this point the supplier should choose not to label

According to Definition 3 we will verify whether co-operative game is superadditive as follows

Proposition 2 Cooperative game (N v) is superadditive

Proof In fact the manufacturer will not profit if it does nottake the supplierrsquos resource Hence we can infer thatv( i ) v( j1113864 1113865) 0 i j isin AB If supplier M cooperateswith manufacturer i then

v( M i ) v( M i j1113864 1113865)gt 0 (6)

hence v( j1113864 1113865) + v( M i )le v( M i j1113864 1113865) +us we derive thefollowing

v C1( 1113857 + v C2( 1113857le v C1 cupC2( 1113857 (7)

As a result cooperative game (N v) is superadditive

+e superadditivity of the cooperative game shows thatall players in the game are willing to cooperate because thetotal revenue from cooperation is always no less than thesum of the revenue from their respective operations +isnotion also proves the feasibility and rationality of themodel

In this subsection we dissect the supplierrsquos labelingdecision without considering the manufacturersrsquo advertisinginvestment and verify the superadditivity of the cooperativealliance Next we will establish the AIGM to further studythe investment decisions of the supplier and manufacturerswhen considering advertising investment

32 AIGM To increase competitiveness the manufacturerswill advertise their products On the basis of the BIGM weestablish the AIGM to further study the impact of adver-tising investment on the decision of supply chain membersWe assume that manufacturers A and B have the ability toadvertise their products Figure 4 shows the prices of themanufacturersrsquo products in the BIGM and AIGM

Supplier M decideswhether to label

Manufacturer goesinto production

Noncooperative stage Cooperative stage

Supplier and manufacturerdivide profit

Figure 1 Decision sequence of players in BIGM

Supplier MA B

0 0

0 0

No label

PA

PAPB + αBc0

(12)

PB

Label

A B

Figure 2 Prices of manufacturersrsquo product in BIGM

Supplier M

No label

Label

[PB PA]

[PB + αBc0(12) ndash c0 PA ndash c0]

Figure 3 Income range of supplier M in BIGM

Table 1 Supplierrsquos optimal decision in BIGM

Condition Decisionc0 lt (136)α2B and c0 lt ((PA minus PB)αB)2 Labelc0 ge (136)α2B No label

Table 2 Expected profit of supplier M in BIGM

SM π1MNo label πN1M (12)PA + (16)PBLabel πL1M (12)PA + (16)(PB + αBc

(12)0 ) minus c0

Complexity 5

In the noncooperative stage (S1 Sn) supplier Mdecides whether to label whereas manufacturers A and Bdecide whether to invest in advertising and how much toinvest In the cooperative stage (N v) the supplier andmanufacturers divide the profit Figure 5 illustrates thedecision sequence in the AIGM

In the analysis of the biform game (SA SB SM N v) weadopt the backwards induction which is contrary to thedecision order First profit set (πA πB πM) under strategyset (SA SB SM) is calculated using the Shapley valuemethod+en the optimal decision of the manufacturer onadvertising investment is obtained by analyzing theseprofits Finally we obtain the labeling decision of thesupplier

Figure 6 provides the income ranges of supplierM In thecase of manufacturers A and B investing in advertising ifsupplier M chooses not to label and cooperates withmanufacturer A then the total revenue is PA + αAc

(12)A minus cA

and manufacturer B gains no benefit However if supplier Mcooperates with manufacturer B then the total revenue isPB + αBc

(12)B minus cB +us the income range of supplier M in

this case is [PB + αBc(12)B minus cB PA + αAc

(12)A minus cA] If supplier

M chooses to label and cooperates with manufacturer Athen the total revenue will be PA + αAc

(12)A minus c0 minus cA If

supplier M cooperates with manufacturer B then the totalrevenue will be PB + αB(c0 + cB)(12) minus c0 minus cB In this casethe income range of supplier M is [PB + αB(c0 + cB)(12)minus

c0 minus cB PA + αAc(12)A minus c0 minus cA]

Notably however if one or both manufacturers do notinvest in advertising the supplierrsquos income range will be-come more complex Consequently we will analyze theinvestment decisions of the manufacturers

Proposition 3 Manufacturers A and B choose to invest inadvertising in AIGM

Proof When supplier M chooses not to label we can obtainthe profit of manufacturer B using the formula in Definition2 as follows

πN2B 16

PB + αBc(12)B1113872 1113873 minus cB (8)

Understanding that manufacturer Brsquos profit is only re-lated to its investment is easy that is advertising investmentcan bring positive net income to B +us manufacturer Bwill choose to invest in advertising +en we analyze Arsquosinvestment decision as follows

πN2A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus cA (9)

Under the premise that manufacturer B must invest inadvertising advertising investment can also bring positive netincome to manufacturer A who will also invest in advertisingat this moment +erefore manufacturers A and B will investin advertising when supplier M chooses not to label

Similarly when supplier M chooses to label we obtain

πL2B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cB

πL2A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cA

(10)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in AIGM

Proposition 3 indicates that both manufacturers shouldactively invest in advertising to strengthen competitivenessin the face of the existence of a competitor which equalsequilibrium in the dominant strategy by the competitivegame between two manufacturers Notably howeveroverinvestment may adversely affect manufacturers becauseexcessive investment will not only reduce the manufacturersrsquoshort-term operating capital but also damage profit and leadto bankruptcy +erefore manufacturers should furthermake a decision on the optimal levels of advertising in-vestment namely clowastA and clowastB In the following discussion wewill highlight each manufacturerrsquos optimal advertising in-vestment level under various strategies

Proposition 4 Table 3 presents the optimal amount of eachmanufacturerrsquo advertising investment

Proof We can obtain the manufacturersrsquo expected profitunder the different decisions of supplier M using the Shapleyvalue method When supplier M chooses not to label we canderive cNlowastA (116)α2A and cNlowastB (1144)α2B by calculatingdπN

2AdcA 0 and dπN2BdcB 0 respectively Similarlywhen M chooses to label we can obtain cLlowastA (116)α2A andcLlowastB (1144)α2B minus c0

Analysis of the manufacturersrsquo optimal advertising in-vestment level indicates that manufacturer heterogeneity can

A B

0 0

0 0

No label

Label0 0

0 0

No label

Label

A B

AIGM

BIGM

PA

PA

PB

PA + αAcA(12)

PA + αAcA(12)

PB + αB(c0 + cB)(12)

PB + αBcB(12)

PB + αBc0(12)

Figure 4 Prices of manufacturersrsquo products in BIGM and AIGM

6 Complexity

lead to differentiation of investment decisions +e supplierrsquosdecision to label has no effect onmanufacturer Arsquos investmentbut reduces manufacturer Brsquos investment According to As-sumption (4) in Section 2 labeling does not change the priceof manufacturer Arsquos products and will not thus affect man-ufacturer Arsquos decision However supplierMrsquos decision to labelwill increase the price of manufacturer Brsquos products whichindicates that the supplier partially undertakes the re-sponsibility that jointly improves the value of the products Inthis manner manufacturer Brsquos view that is ldquodiffusion ofresponsibilityrdquo is triggered and can be used to denote thepsyche of one who wants to decrease his responsibility at theexpense of the partnerrsquos efforts+erefore manufacturer Bwillreduce his investment level when supplier M chooses to labelHorizontally regardless of whether the supplier decides tolabels or not the well-known manufacturer will always investmore in advertising compared with the weaker manufacturerbecause the well-known manufacturer wants to consolidatecompetitiveness and attractsmore attention from the supplierIn summary the weaker manufacturer should appropriatelyreduce its investment in advertising when the supplier choosesto label whereas the well-known manufacturer should retainits investment level to be always higher than that of the weakermanufacturer to solidify its market position andcompetitiveness

We will further discuss the supplierrsquos decision to label inthe face of the manufacturersrsquo equilibrium strategies

Proposition 5 Considering advertising investment supplierM always chooses not to label

Proof According to Table 4 we find that πN2M minus πL

2M c0 gt 0+erefore supplier M who pursues maximum profit alwaysopts not to label

From the perspective of the individual interests of de-cision makers and in the face of the manufacturersrsquo in-vestment efforts the supplier will generate the ldquodiffusion ofresponsibilityrdquo mindset and choose not to label to minimizeits investment From the perspective of the overall interest ofthe supply chain when the manufacturers contribute to thecooperative alliance through advertising investment thesupplierrsquos active investment behavior that it still chooses tolabel may let the total investment outweigh the total returnand enter the stage of diminishing returns on scale Intheory the competitive game equilibrium result that allmanufacturers invest in advertising improves the supplierrsquosadvantage in the cooperative game which leads to the co-operative game equilibrium result where the supplier doesnot need to label

In this subsection we set up the AIGM and use theShapley value method to calculate the profit of each playerunder different scenarios and finally obtain optimal de-cisions by backwards induction Finding shows that in thetripartite game with advertising investment between onesupplier and two heterogeneous manufacturers the lattershould invest in advertising to enhance competitivenessand the possibility of cooperation with the supplier Doingso will contribute to improving the value of products suchthat the supplier does not need to label In the followingsubsection we will verify the existence of the un-derinvestment problem and further shed light on theoptimal decisions of the supplier and manufacturers inASM

33 ASM +e supplier usually gives the manufacturers anincentive policy to stimulate investment In this subsectionwe introduce the advertising subsidy mechanism where thesupplier will commit to pay a certain percentage of themanufacturersrsquo advertising investment Figure 7 providesthe decision sequence in ASM

For ease of distinction we denote π2j and π3j to rep-resent the profit of j in the AIGM and ASM respectivelywhere j isin MAB ti refers to the supplierrsquos subsidy per-centage for the manufacturerrsquos advertising investment

Supplier M decideswhether to label

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decidewhether to investin advertising and

how much to invest

Figure 5 Decision sequence of players in AIGM

Supplier M

No label

Label

[PB + αBcB(12) ndash cB PA + αAcA

(12) ndash cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash cB PA + αAcA(12) ndash c0 ndash cA]

Figure 6 Income ranges of supplier M in AIGM

Table 3 Optimal amount of advertising investment

SM clowastA clowastB

No label (116)α2A (1144)α2BLabel (116)α2A (1144)α2B minus c0

Table 4 Expected benefits of supplier M in AIGM

SM π2MNo label πN2M (12)PA + (16)PB + (18)α2A + (172)α2BLabel πL2M (12)PA + (16)PB + (18)α2A + (172)α2B minus c0

Complexity 7

+erefore we can express the advertising subsidy mecha-nism as follows

π3A π2A + tAcA

π3B π2B + tBcB

π3M π2M minus tAcA minus tBcB

(11)

Considering the effect of subsidy on earnings based onthe AIGM we obtain the income range of the supplier inASM as shown in Figure 8

Using the same method of analysis in the AIGM weobtain the optimum decisions of the supplier and manu-facturers First we analyze whether the manufacturers willchoose to invest in advertising in ASM

Proposition 6 Manufacturers A and B choose to invest inadvertising in ASM

Proof When supplier M chooses not to label manufacturerBrsquos profits can be acquired by the Shapley value method asfollows

πN3B

16

PB + αBc(12)B1113872 1113873 minus 1 minus tB( 1113857cB (12)

Finding that manufacturer Brsquos profit is only related to itsinvestment and advertising investment can bring a positivenet income to manufacturer B is easy to understand +usmanufacturer B will choose to invest in advertising+en weanalyze manufacturer Arsquos investment decision and derive itsprofit as follows

πN3A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus 1 minus tA( 1113857cA

(13)

Under the premise that manufacturer B must invest inadvertising manufacturer A can derive positive net incomefrom advertising investment+erefore manufacturer A willalso invest in advertising

Similarly when supplier M chooses to label we have

πL3B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus 1 minus tB( 1113857cB (14)

πL3A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus 1 minus tA( 1113857cA

(15)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in ASM

We find that under the advertising subsidy mechanismthe manufacturers will still choose to invest in advertising Inaddition we can speculate that the manufacturers are morewilling to invest because the subsidy is harmless and ben-eficial to them +erefore the manufacturers may increaseinvestment under the advertising subsidy mechanism Nextwe will verify whether subsidy will promote the manufac-turersrsquo investment by analyzing the manufacturersrsquo optimalinvestment level and elucidate the optimal subsidy strategy

Proposition 7 Table 5 presents the optimal decisions ofplayers in ASM

Proof We can obtain the profit functions of the supplierunder different circumstances using the Shapley valuemethod When the supplier chooses not to label then

πN3M

12

PA + αAc(12)A1113872 1113873 +

16

PB + αBc(12)B1113872 1113873 minus tAcA minus tBcB

(16)

Otherwise

πL3M 12

PA + αAc(12)A1113872 1113873 +

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus tAcA minus tBcB minus c0

(17)

Based on equations (12)ndash(17) we can obtain the optimaldecisions of advertising investment and subsidy When Mchooses not to label we can derive cNlowastA α2A(16(1 minus tA)2)

and cNlowastB α2B(144(1 minus tB)2) from dπN3AdcA 0 and fromdπN

3BdcB 0 respectively +en we can obtain tNlowastA 13and tNlowastB 13 from zπN3MztA 0 and from zπN

3MztB 0respectively +erefore we have cNlowastA (964)α2A andcNlowastB (164)α2B

When supplier M opts to label we can derive cLlowastA

α2A(16(1 minus tA)2) and cLlowastB α2B(144(1 minus tB)2) minus c0 fromdπL

3AdcA 0 and from dπL3BdcB 0 respectively +en wehave tLlowastA 13 from zπL

3MztA 0 Based on zπL3MztB 0

we find that tLlowastB satisfies

α2B 1 minus 3tB( 1113857 + 144c0 1 minus tB( 11138573

0 (18)

Supplier M decideswhether to label

Supplier M decideswhether to grant subsidy

and how much to subsidize

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decide whetherto invest in advertising and

how much to invest

Figure 7 Decision sequence of players in ASM

8 Complexity

Based on Equation (18) and cLlowastB α2B(144(1 minus tB)2) minus c0we have the following

tLlowastB 1 +

112

α2BK

minusK

c01113888 1113889

K 12c20α

2B +

144c40α4B + c30α6B1113969

1113874 1113875(13)

gt 0 (19)

cLlowastB

c0 3c0α2BK2 + K 12c20α2B minus K3( 1113857 minus c20α

2B α2B + 12K( 1113857( 1113857

K2 minus c0α2B( 11138572

(20)From Equation (18) and cLlowastB ge 0 we derive (3tLlowastB minus 1)

(2tLlowastB minus 1)le 0 as follows13le t

LlowastB le

12 (21)

First we analyze the optimal subsidy strategy of supplieraccording to Proposition 7 Longitudinally the subsidy formanufacturer B when supplier M chooses to label is higherthan that of the opposite Based on Proposition 4 manu-facturer B emerges with the ldquodiffusion of responsibilityrdquomindset in the face of the supplierrsquos decision to label+erefore supplier M will endowmanufacturer B with moresubsidies in an attempt to eliminate the mindset as much aspossible Horizontally when supplier M chooses to label thesubsidy to manufacturer B is higher than that to manu-facturer A because the supplier wants to improve his bar-gaining power in the negotiation with manufacturer A byclaiming to give more subsidies to manufacturer B

+en we analyze the optimal advertising investmentdecision of manufacturers When supplier chooses not tolabel the well-known manufacturer invests more than theweaker manufacturer to attract more attention from thesupplier +erefore the well-known manufacturer shouldalways retain its investment level to be higher than that of theweaker manufacturer to consolidate its market position Insummary supplier should endow the weaker manufacturerwith more subsidies when labeling and the well-knownmanufacturer should invest more than the weaker manu-facturer when supplier chooses not to label

Corollary 1 When supplier M chooses not to label anunderinvestment problem underlies the manufacturerrsquos ad-vertising investment In response subsidy can stimulate themanufacturersrsquo investment and mitigate the underinvestmentproblem

Proof By comparing the corresponding investment levels inTables 3 and 5 Corollary 1 can be proved For examplewhen supplier M chooses not to label manufacturer Arsquosoptimal investment levels in AIGM and ASM are (116)α2Aand (964)α2A as shown in Tables 3 and 5 respectively+erefore manufacturer Arsquos investment level in the AIGM isless than that in the ASM which reflects the un-derinvestment problem In addition subsidy can increasethe investment level of manufacturer A by (564)α2A

Corollary 1 confirms the existence of the un-derinvestment problem and shows that subsidy can stim-ulate manufacturersrsquo advertising investment level whichproves the importance of subsidy in coordinating the supplychain Finally we will further investigate the influence ofsubsidy on the supplier

Proposition 8 When the supplier chooses not to label thesubsidy strategy has a positive impact on the supplier suchthat the supplier will unconditionally issue subsidy to themanufacturers

Proof In the previous analysis we obtain the profits ofsupplier M when it does and does not grant subsidy If thesupplier chooses not to label then

πN3M minus πN2M

1576

9α2A + α2B1113872 1113873gt 0 (22)

We find that πN3M is always higher than πN2M which

indicates that the subsidy strategy has a positive impact onthe supplier who will unconditionally issue subsidy to themanufacturers when it opts not to label

In the ASM the advertising subsidy issued by thesupplier first promotes the investment of the manufacturersthat is the higher the investment the more improved thevalue of the products +is scenario thereby increases thebenefits of the cooperative alliance and ultimately improvesthe supplierrsquos profit+erefore the supplier should stimulatethe manufacturersrsquo investment by granting subsidies toincrease the intensity and promote the positive shift inequilibrium results of the competitive game so as to gainmore benefits in the next cooperative game In addition the

Supplier M

No label

Label

[PB + αBcB(12) ndash (1 + tB)cB PA + αAcA

(12) ndash (1 + tA)cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash (1 + tB)cB PA + αAcA(12) ndash c0 ndash (1 + tA)cA]

Figure 8 Income range of supplier in ASM

Table 5 Optimal decisions of players in ASM

SM clowastA clowastB tlowastA tlowastB

No label (964)α2A (164)α2B 13 13Label (964)α2A (α2B(144(1 minus tLlowastB )2)) minus c0 13 [13 12]

Complexity 9

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

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Mathematical Problems in Engineering

Applied MathematicsJournal of

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Submit your manuscripts atwwwhindawicom

In the noncooperative stage (S1 Sn) supplier Mdecides whether to label whereas manufacturers A and Bdecide whether to invest in advertising and how much toinvest In the cooperative stage (N v) the supplier andmanufacturers divide the profit Figure 5 illustrates thedecision sequence in the AIGM

In the analysis of the biform game (SA SB SM N v) weadopt the backwards induction which is contrary to thedecision order First profit set (πA πB πM) under strategyset (SA SB SM) is calculated using the Shapley valuemethod+en the optimal decision of the manufacturer onadvertising investment is obtained by analyzing theseprofits Finally we obtain the labeling decision of thesupplier

Figure 6 provides the income ranges of supplierM In thecase of manufacturers A and B investing in advertising ifsupplier M chooses not to label and cooperates withmanufacturer A then the total revenue is PA + αAc

(12)A minus cA

and manufacturer B gains no benefit However if supplier Mcooperates with manufacturer B then the total revenue isPB + αBc

(12)B minus cB +us the income range of supplier M in

this case is [PB + αBc(12)B minus cB PA + αAc

(12)A minus cA] If supplier

M chooses to label and cooperates with manufacturer Athen the total revenue will be PA + αAc

(12)A minus c0 minus cA If

supplier M cooperates with manufacturer B then the totalrevenue will be PB + αB(c0 + cB)(12) minus c0 minus cB In this casethe income range of supplier M is [PB + αB(c0 + cB)(12)minus

c0 minus cB PA + αAc(12)A minus c0 minus cA]

Notably however if one or both manufacturers do notinvest in advertising the supplierrsquos income range will be-come more complex Consequently we will analyze theinvestment decisions of the manufacturers

Proposition 3 Manufacturers A and B choose to invest inadvertising in AIGM

Proof When supplier M chooses not to label we can obtainthe profit of manufacturer B using the formula in Definition2 as follows

πN2B 16

PB + αBc(12)B1113872 1113873 minus cB (8)

Understanding that manufacturer Brsquos profit is only re-lated to its investment is easy that is advertising investmentcan bring positive net income to B +us manufacturer Bwill choose to invest in advertising +en we analyze Arsquosinvestment decision as follows

πN2A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus cA (9)

Under the premise that manufacturer B must invest inadvertising advertising investment can also bring positive netincome to manufacturer A who will also invest in advertisingat this moment +erefore manufacturers A and B will investin advertising when supplier M chooses not to label

Similarly when supplier M chooses to label we obtain

πL2B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cB

πL2A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus cA

(10)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in AIGM

Proposition 3 indicates that both manufacturers shouldactively invest in advertising to strengthen competitivenessin the face of the existence of a competitor which equalsequilibrium in the dominant strategy by the competitivegame between two manufacturers Notably howeveroverinvestment may adversely affect manufacturers becauseexcessive investment will not only reduce the manufacturersrsquoshort-term operating capital but also damage profit and leadto bankruptcy +erefore manufacturers should furthermake a decision on the optimal levels of advertising in-vestment namely clowastA and clowastB In the following discussion wewill highlight each manufacturerrsquos optimal advertising in-vestment level under various strategies

Proposition 4 Table 3 presents the optimal amount of eachmanufacturerrsquo advertising investment

Proof We can obtain the manufacturersrsquo expected profitunder the different decisions of supplier M using the Shapleyvalue method When supplier M chooses not to label we canderive cNlowastA (116)α2A and cNlowastB (1144)α2B by calculatingdπN

2AdcA 0 and dπN2BdcB 0 respectively Similarlywhen M chooses to label we can obtain cLlowastA (116)α2A andcLlowastB (1144)α2B minus c0

Analysis of the manufacturersrsquo optimal advertising in-vestment level indicates that manufacturer heterogeneity can

A B

0 0

0 0

No label

Label0 0

0 0

No label

Label

A B

AIGM

BIGM

PA

PA

PB

PA + αAcA(12)

PA + αAcA(12)

PB + αB(c0 + cB)(12)

PB + αBcB(12)

PB + αBc0(12)

Figure 4 Prices of manufacturersrsquo products in BIGM and AIGM

6 Complexity

lead to differentiation of investment decisions +e supplierrsquosdecision to label has no effect onmanufacturer Arsquos investmentbut reduces manufacturer Brsquos investment According to As-sumption (4) in Section 2 labeling does not change the priceof manufacturer Arsquos products and will not thus affect man-ufacturer Arsquos decision However supplierMrsquos decision to labelwill increase the price of manufacturer Brsquos products whichindicates that the supplier partially undertakes the re-sponsibility that jointly improves the value of the products Inthis manner manufacturer Brsquos view that is ldquodiffusion ofresponsibilityrdquo is triggered and can be used to denote thepsyche of one who wants to decrease his responsibility at theexpense of the partnerrsquos efforts+erefore manufacturer Bwillreduce his investment level when supplier M chooses to labelHorizontally regardless of whether the supplier decides tolabels or not the well-known manufacturer will always investmore in advertising compared with the weaker manufacturerbecause the well-known manufacturer wants to consolidatecompetitiveness and attractsmore attention from the supplierIn summary the weaker manufacturer should appropriatelyreduce its investment in advertising when the supplier choosesto label whereas the well-known manufacturer should retainits investment level to be always higher than that of the weakermanufacturer to solidify its market position andcompetitiveness

We will further discuss the supplierrsquos decision to label inthe face of the manufacturersrsquo equilibrium strategies

Proposition 5 Considering advertising investment supplierM always chooses not to label

Proof According to Table 4 we find that πN2M minus πL

2M c0 gt 0+erefore supplier M who pursues maximum profit alwaysopts not to label

From the perspective of the individual interests of de-cision makers and in the face of the manufacturersrsquo in-vestment efforts the supplier will generate the ldquodiffusion ofresponsibilityrdquo mindset and choose not to label to minimizeits investment From the perspective of the overall interest ofthe supply chain when the manufacturers contribute to thecooperative alliance through advertising investment thesupplierrsquos active investment behavior that it still chooses tolabel may let the total investment outweigh the total returnand enter the stage of diminishing returns on scale Intheory the competitive game equilibrium result that allmanufacturers invest in advertising improves the supplierrsquosadvantage in the cooperative game which leads to the co-operative game equilibrium result where the supplier doesnot need to label

In this subsection we set up the AIGM and use theShapley value method to calculate the profit of each playerunder different scenarios and finally obtain optimal de-cisions by backwards induction Finding shows that in thetripartite game with advertising investment between onesupplier and two heterogeneous manufacturers the lattershould invest in advertising to enhance competitivenessand the possibility of cooperation with the supplier Doingso will contribute to improving the value of products suchthat the supplier does not need to label In the followingsubsection we will verify the existence of the un-derinvestment problem and further shed light on theoptimal decisions of the supplier and manufacturers inASM

33 ASM +e supplier usually gives the manufacturers anincentive policy to stimulate investment In this subsectionwe introduce the advertising subsidy mechanism where thesupplier will commit to pay a certain percentage of themanufacturersrsquo advertising investment Figure 7 providesthe decision sequence in ASM

For ease of distinction we denote π2j and π3j to rep-resent the profit of j in the AIGM and ASM respectivelywhere j isin MAB ti refers to the supplierrsquos subsidy per-centage for the manufacturerrsquos advertising investment

Supplier M decideswhether to label

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decidewhether to investin advertising and

how much to invest

Figure 5 Decision sequence of players in AIGM

Supplier M

No label

Label

[PB + αBcB(12) ndash cB PA + αAcA

(12) ndash cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash cB PA + αAcA(12) ndash c0 ndash cA]

Figure 6 Income ranges of supplier M in AIGM

Table 3 Optimal amount of advertising investment

SM clowastA clowastB

No label (116)α2A (1144)α2BLabel (116)α2A (1144)α2B minus c0

Table 4 Expected benefits of supplier M in AIGM

SM π2MNo label πN2M (12)PA + (16)PB + (18)α2A + (172)α2BLabel πL2M (12)PA + (16)PB + (18)α2A + (172)α2B minus c0

Complexity 7

+erefore we can express the advertising subsidy mecha-nism as follows

π3A π2A + tAcA

π3B π2B + tBcB

π3M π2M minus tAcA minus tBcB

(11)

Considering the effect of subsidy on earnings based onthe AIGM we obtain the income range of the supplier inASM as shown in Figure 8

Using the same method of analysis in the AIGM weobtain the optimum decisions of the supplier and manu-facturers First we analyze whether the manufacturers willchoose to invest in advertising in ASM

Proposition 6 Manufacturers A and B choose to invest inadvertising in ASM

Proof When supplier M chooses not to label manufacturerBrsquos profits can be acquired by the Shapley value method asfollows

πN3B

16

PB + αBc(12)B1113872 1113873 minus 1 minus tB( 1113857cB (12)

Finding that manufacturer Brsquos profit is only related to itsinvestment and advertising investment can bring a positivenet income to manufacturer B is easy to understand +usmanufacturer B will choose to invest in advertising+en weanalyze manufacturer Arsquos investment decision and derive itsprofit as follows

πN3A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus 1 minus tA( 1113857cA

(13)

Under the premise that manufacturer B must invest inadvertising manufacturer A can derive positive net incomefrom advertising investment+erefore manufacturer A willalso invest in advertising

Similarly when supplier M chooses to label we have

πL3B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus 1 minus tB( 1113857cB (14)

πL3A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus 1 minus tA( 1113857cA

(15)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in ASM

We find that under the advertising subsidy mechanismthe manufacturers will still choose to invest in advertising Inaddition we can speculate that the manufacturers are morewilling to invest because the subsidy is harmless and ben-eficial to them +erefore the manufacturers may increaseinvestment under the advertising subsidy mechanism Nextwe will verify whether subsidy will promote the manufac-turersrsquo investment by analyzing the manufacturersrsquo optimalinvestment level and elucidate the optimal subsidy strategy

Proposition 7 Table 5 presents the optimal decisions ofplayers in ASM

Proof We can obtain the profit functions of the supplierunder different circumstances using the Shapley valuemethod When the supplier chooses not to label then

πN3M

12

PA + αAc(12)A1113872 1113873 +

16

PB + αBc(12)B1113872 1113873 minus tAcA minus tBcB

(16)

Otherwise

πL3M 12

PA + αAc(12)A1113872 1113873 +

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus tAcA minus tBcB minus c0

(17)

Based on equations (12)ndash(17) we can obtain the optimaldecisions of advertising investment and subsidy When Mchooses not to label we can derive cNlowastA α2A(16(1 minus tA)2)

and cNlowastB α2B(144(1 minus tB)2) from dπN3AdcA 0 and fromdπN

3BdcB 0 respectively +en we can obtain tNlowastA 13and tNlowastB 13 from zπN3MztA 0 and from zπN

3MztB 0respectively +erefore we have cNlowastA (964)α2A andcNlowastB (164)α2B

When supplier M opts to label we can derive cLlowastA

α2A(16(1 minus tA)2) and cLlowastB α2B(144(1 minus tB)2) minus c0 fromdπL

3AdcA 0 and from dπL3BdcB 0 respectively +en wehave tLlowastA 13 from zπL

3MztA 0 Based on zπL3MztB 0

we find that tLlowastB satisfies

α2B 1 minus 3tB( 1113857 + 144c0 1 minus tB( 11138573

0 (18)

Supplier M decideswhether to label

Supplier M decideswhether to grant subsidy

and how much to subsidize

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decide whetherto invest in advertising and

how much to invest

Figure 7 Decision sequence of players in ASM

8 Complexity

Based on Equation (18) and cLlowastB α2B(144(1 minus tB)2) minus c0we have the following

tLlowastB 1 +

112

α2BK

minusK

c01113888 1113889

K 12c20α

2B +

144c40α4B + c30α6B1113969

1113874 1113875(13)

gt 0 (19)

cLlowastB

c0 3c0α2BK2 + K 12c20α2B minus K3( 1113857 minus c20α

2B α2B + 12K( 1113857( 1113857

K2 minus c0α2B( 11138572

(20)From Equation (18) and cLlowastB ge 0 we derive (3tLlowastB minus 1)

(2tLlowastB minus 1)le 0 as follows13le t

LlowastB le

12 (21)

First we analyze the optimal subsidy strategy of supplieraccording to Proposition 7 Longitudinally the subsidy formanufacturer B when supplier M chooses to label is higherthan that of the opposite Based on Proposition 4 manu-facturer B emerges with the ldquodiffusion of responsibilityrdquomindset in the face of the supplierrsquos decision to label+erefore supplier M will endowmanufacturer B with moresubsidies in an attempt to eliminate the mindset as much aspossible Horizontally when supplier M chooses to label thesubsidy to manufacturer B is higher than that to manu-facturer A because the supplier wants to improve his bar-gaining power in the negotiation with manufacturer A byclaiming to give more subsidies to manufacturer B

+en we analyze the optimal advertising investmentdecision of manufacturers When supplier chooses not tolabel the well-known manufacturer invests more than theweaker manufacturer to attract more attention from thesupplier +erefore the well-known manufacturer shouldalways retain its investment level to be higher than that of theweaker manufacturer to consolidate its market position Insummary supplier should endow the weaker manufacturerwith more subsidies when labeling and the well-knownmanufacturer should invest more than the weaker manu-facturer when supplier chooses not to label

Corollary 1 When supplier M chooses not to label anunderinvestment problem underlies the manufacturerrsquos ad-vertising investment In response subsidy can stimulate themanufacturersrsquo investment and mitigate the underinvestmentproblem

Proof By comparing the corresponding investment levels inTables 3 and 5 Corollary 1 can be proved For examplewhen supplier M chooses not to label manufacturer Arsquosoptimal investment levels in AIGM and ASM are (116)α2Aand (964)α2A as shown in Tables 3 and 5 respectively+erefore manufacturer Arsquos investment level in the AIGM isless than that in the ASM which reflects the un-derinvestment problem In addition subsidy can increasethe investment level of manufacturer A by (564)α2A

Corollary 1 confirms the existence of the un-derinvestment problem and shows that subsidy can stim-ulate manufacturersrsquo advertising investment level whichproves the importance of subsidy in coordinating the supplychain Finally we will further investigate the influence ofsubsidy on the supplier

Proposition 8 When the supplier chooses not to label thesubsidy strategy has a positive impact on the supplier suchthat the supplier will unconditionally issue subsidy to themanufacturers

Proof In the previous analysis we obtain the profits ofsupplier M when it does and does not grant subsidy If thesupplier chooses not to label then

πN3M minus πN2M

1576

9α2A + α2B1113872 1113873gt 0 (22)

We find that πN3M is always higher than πN2M which

indicates that the subsidy strategy has a positive impact onthe supplier who will unconditionally issue subsidy to themanufacturers when it opts not to label

In the ASM the advertising subsidy issued by thesupplier first promotes the investment of the manufacturersthat is the higher the investment the more improved thevalue of the products +is scenario thereby increases thebenefits of the cooperative alliance and ultimately improvesthe supplierrsquos profit+erefore the supplier should stimulatethe manufacturersrsquo investment by granting subsidies toincrease the intensity and promote the positive shift inequilibrium results of the competitive game so as to gainmore benefits in the next cooperative game In addition the

Supplier M

No label

Label

[PB + αBcB(12) ndash (1 + tB)cB PA + αAcA

(12) ndash (1 + tA)cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash (1 + tB)cB PA + αAcA(12) ndash c0 ndash (1 + tA)cA]

Figure 8 Income range of supplier in ASM

Table 5 Optimal decisions of players in ASM

SM clowastA clowastB tlowastA tlowastB

No label (964)α2A (164)α2B 13 13Label (964)α2A (α2B(144(1 minus tLlowastB )2)) minus c0 13 [13 12]

Complexity 9

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

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lead to differentiation of investment decisions +e supplierrsquosdecision to label has no effect onmanufacturer Arsquos investmentbut reduces manufacturer Brsquos investment According to As-sumption (4) in Section 2 labeling does not change the priceof manufacturer Arsquos products and will not thus affect man-ufacturer Arsquos decision However supplierMrsquos decision to labelwill increase the price of manufacturer Brsquos products whichindicates that the supplier partially undertakes the re-sponsibility that jointly improves the value of the products Inthis manner manufacturer Brsquos view that is ldquodiffusion ofresponsibilityrdquo is triggered and can be used to denote thepsyche of one who wants to decrease his responsibility at theexpense of the partnerrsquos efforts+erefore manufacturer Bwillreduce his investment level when supplier M chooses to labelHorizontally regardless of whether the supplier decides tolabels or not the well-known manufacturer will always investmore in advertising compared with the weaker manufacturerbecause the well-known manufacturer wants to consolidatecompetitiveness and attractsmore attention from the supplierIn summary the weaker manufacturer should appropriatelyreduce its investment in advertising when the supplier choosesto label whereas the well-known manufacturer should retainits investment level to be always higher than that of the weakermanufacturer to solidify its market position andcompetitiveness

We will further discuss the supplierrsquos decision to label inthe face of the manufacturersrsquo equilibrium strategies

Proposition 5 Considering advertising investment supplierM always chooses not to label

Proof According to Table 4 we find that πN2M minus πL

2M c0 gt 0+erefore supplier M who pursues maximum profit alwaysopts not to label

From the perspective of the individual interests of de-cision makers and in the face of the manufacturersrsquo in-vestment efforts the supplier will generate the ldquodiffusion ofresponsibilityrdquo mindset and choose not to label to minimizeits investment From the perspective of the overall interest ofthe supply chain when the manufacturers contribute to thecooperative alliance through advertising investment thesupplierrsquos active investment behavior that it still chooses tolabel may let the total investment outweigh the total returnand enter the stage of diminishing returns on scale Intheory the competitive game equilibrium result that allmanufacturers invest in advertising improves the supplierrsquosadvantage in the cooperative game which leads to the co-operative game equilibrium result where the supplier doesnot need to label

In this subsection we set up the AIGM and use theShapley value method to calculate the profit of each playerunder different scenarios and finally obtain optimal de-cisions by backwards induction Finding shows that in thetripartite game with advertising investment between onesupplier and two heterogeneous manufacturers the lattershould invest in advertising to enhance competitivenessand the possibility of cooperation with the supplier Doingso will contribute to improving the value of products suchthat the supplier does not need to label In the followingsubsection we will verify the existence of the un-derinvestment problem and further shed light on theoptimal decisions of the supplier and manufacturers inASM

33 ASM +e supplier usually gives the manufacturers anincentive policy to stimulate investment In this subsectionwe introduce the advertising subsidy mechanism where thesupplier will commit to pay a certain percentage of themanufacturersrsquo advertising investment Figure 7 providesthe decision sequence in ASM

For ease of distinction we denote π2j and π3j to rep-resent the profit of j in the AIGM and ASM respectivelywhere j isin MAB ti refers to the supplierrsquos subsidy per-centage for the manufacturerrsquos advertising investment

Supplier M decideswhether to label

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decidewhether to investin advertising and

how much to invest

Figure 5 Decision sequence of players in AIGM

Supplier M

No label

Label

[PB + αBcB(12) ndash cB PA + αAcA

(12) ndash cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash cB PA + αAcA(12) ndash c0 ndash cA]

Figure 6 Income ranges of supplier M in AIGM

Table 3 Optimal amount of advertising investment

SM clowastA clowastB

No label (116)α2A (1144)α2BLabel (116)α2A (1144)α2B minus c0

Table 4 Expected benefits of supplier M in AIGM

SM π2MNo label πN2M (12)PA + (16)PB + (18)α2A + (172)α2BLabel πL2M (12)PA + (16)PB + (18)α2A + (172)α2B minus c0

Complexity 7

+erefore we can express the advertising subsidy mecha-nism as follows

π3A π2A + tAcA

π3B π2B + tBcB

π3M π2M minus tAcA minus tBcB

(11)

Considering the effect of subsidy on earnings based onthe AIGM we obtain the income range of the supplier inASM as shown in Figure 8

Using the same method of analysis in the AIGM weobtain the optimum decisions of the supplier and manu-facturers First we analyze whether the manufacturers willchoose to invest in advertising in ASM

Proposition 6 Manufacturers A and B choose to invest inadvertising in ASM

Proof When supplier M chooses not to label manufacturerBrsquos profits can be acquired by the Shapley value method asfollows

πN3B

16

PB + αBc(12)B1113872 1113873 minus 1 minus tB( 1113857cB (12)

Finding that manufacturer Brsquos profit is only related to itsinvestment and advertising investment can bring a positivenet income to manufacturer B is easy to understand +usmanufacturer B will choose to invest in advertising+en weanalyze manufacturer Arsquos investment decision and derive itsprofit as follows

πN3A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus 1 minus tA( 1113857cA

(13)

Under the premise that manufacturer B must invest inadvertising manufacturer A can derive positive net incomefrom advertising investment+erefore manufacturer A willalso invest in advertising

Similarly when supplier M chooses to label we have

πL3B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus 1 minus tB( 1113857cB (14)

πL3A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus 1 minus tA( 1113857cA

(15)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in ASM

We find that under the advertising subsidy mechanismthe manufacturers will still choose to invest in advertising Inaddition we can speculate that the manufacturers are morewilling to invest because the subsidy is harmless and ben-eficial to them +erefore the manufacturers may increaseinvestment under the advertising subsidy mechanism Nextwe will verify whether subsidy will promote the manufac-turersrsquo investment by analyzing the manufacturersrsquo optimalinvestment level and elucidate the optimal subsidy strategy

Proposition 7 Table 5 presents the optimal decisions ofplayers in ASM

Proof We can obtain the profit functions of the supplierunder different circumstances using the Shapley valuemethod When the supplier chooses not to label then

πN3M

12

PA + αAc(12)A1113872 1113873 +

16

PB + αBc(12)B1113872 1113873 minus tAcA minus tBcB

(16)

Otherwise

πL3M 12

PA + αAc(12)A1113872 1113873 +

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus tAcA minus tBcB minus c0

(17)

Based on equations (12)ndash(17) we can obtain the optimaldecisions of advertising investment and subsidy When Mchooses not to label we can derive cNlowastA α2A(16(1 minus tA)2)

and cNlowastB α2B(144(1 minus tB)2) from dπN3AdcA 0 and fromdπN

3BdcB 0 respectively +en we can obtain tNlowastA 13and tNlowastB 13 from zπN3MztA 0 and from zπN

3MztB 0respectively +erefore we have cNlowastA (964)α2A andcNlowastB (164)α2B

When supplier M opts to label we can derive cLlowastA

α2A(16(1 minus tA)2) and cLlowastB α2B(144(1 minus tB)2) minus c0 fromdπL

3AdcA 0 and from dπL3BdcB 0 respectively +en wehave tLlowastA 13 from zπL

3MztA 0 Based on zπL3MztB 0

we find that tLlowastB satisfies

α2B 1 minus 3tB( 1113857 + 144c0 1 minus tB( 11138573

0 (18)

Supplier M decideswhether to label

Supplier M decideswhether to grant subsidy

and how much to subsidize

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decide whetherto invest in advertising and

how much to invest

Figure 7 Decision sequence of players in ASM

8 Complexity

Based on Equation (18) and cLlowastB α2B(144(1 minus tB)2) minus c0we have the following

tLlowastB 1 +

112

α2BK

minusK

c01113888 1113889

K 12c20α

2B +

144c40α4B + c30α6B1113969

1113874 1113875(13)

gt 0 (19)

cLlowastB

c0 3c0α2BK2 + K 12c20α2B minus K3( 1113857 minus c20α

2B α2B + 12K( 1113857( 1113857

K2 minus c0α2B( 11138572

(20)From Equation (18) and cLlowastB ge 0 we derive (3tLlowastB minus 1)

(2tLlowastB minus 1)le 0 as follows13le t

LlowastB le

12 (21)

First we analyze the optimal subsidy strategy of supplieraccording to Proposition 7 Longitudinally the subsidy formanufacturer B when supplier M chooses to label is higherthan that of the opposite Based on Proposition 4 manu-facturer B emerges with the ldquodiffusion of responsibilityrdquomindset in the face of the supplierrsquos decision to label+erefore supplier M will endowmanufacturer B with moresubsidies in an attempt to eliminate the mindset as much aspossible Horizontally when supplier M chooses to label thesubsidy to manufacturer B is higher than that to manu-facturer A because the supplier wants to improve his bar-gaining power in the negotiation with manufacturer A byclaiming to give more subsidies to manufacturer B

+en we analyze the optimal advertising investmentdecision of manufacturers When supplier chooses not tolabel the well-known manufacturer invests more than theweaker manufacturer to attract more attention from thesupplier +erefore the well-known manufacturer shouldalways retain its investment level to be higher than that of theweaker manufacturer to consolidate its market position Insummary supplier should endow the weaker manufacturerwith more subsidies when labeling and the well-knownmanufacturer should invest more than the weaker manu-facturer when supplier chooses not to label

Corollary 1 When supplier M chooses not to label anunderinvestment problem underlies the manufacturerrsquos ad-vertising investment In response subsidy can stimulate themanufacturersrsquo investment and mitigate the underinvestmentproblem

Proof By comparing the corresponding investment levels inTables 3 and 5 Corollary 1 can be proved For examplewhen supplier M chooses not to label manufacturer Arsquosoptimal investment levels in AIGM and ASM are (116)α2Aand (964)α2A as shown in Tables 3 and 5 respectively+erefore manufacturer Arsquos investment level in the AIGM isless than that in the ASM which reflects the un-derinvestment problem In addition subsidy can increasethe investment level of manufacturer A by (564)α2A

Corollary 1 confirms the existence of the un-derinvestment problem and shows that subsidy can stim-ulate manufacturersrsquo advertising investment level whichproves the importance of subsidy in coordinating the supplychain Finally we will further investigate the influence ofsubsidy on the supplier

Proposition 8 When the supplier chooses not to label thesubsidy strategy has a positive impact on the supplier suchthat the supplier will unconditionally issue subsidy to themanufacturers

Proof In the previous analysis we obtain the profits ofsupplier M when it does and does not grant subsidy If thesupplier chooses not to label then

πN3M minus πN2M

1576

9α2A + α2B1113872 1113873gt 0 (22)

We find that πN3M is always higher than πN2M which

indicates that the subsidy strategy has a positive impact onthe supplier who will unconditionally issue subsidy to themanufacturers when it opts not to label

In the ASM the advertising subsidy issued by thesupplier first promotes the investment of the manufacturersthat is the higher the investment the more improved thevalue of the products +is scenario thereby increases thebenefits of the cooperative alliance and ultimately improvesthe supplierrsquos profit+erefore the supplier should stimulatethe manufacturersrsquo investment by granting subsidies toincrease the intensity and promote the positive shift inequilibrium results of the competitive game so as to gainmore benefits in the next cooperative game In addition the

Supplier M

No label

Label

[PB + αBcB(12) ndash (1 + tB)cB PA + αAcA

(12) ndash (1 + tA)cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash (1 + tB)cB PA + αAcA(12) ndash c0 ndash (1 + tA)cA]

Figure 8 Income range of supplier in ASM

Table 5 Optimal decisions of players in ASM

SM clowastA clowastB tlowastA tlowastB

No label (964)α2A (164)α2B 13 13Label (964)α2A (α2B(144(1 minus tLlowastB )2)) minus c0 13 [13 12]

Complexity 9

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

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Mathematical Problems in Engineering

Applied MathematicsJournal of

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Complex AnalysisJournal of

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OptimizationJournal of

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Stochastic AnalysisInternational Journal of

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+erefore we can express the advertising subsidy mecha-nism as follows

π3A π2A + tAcA

π3B π2B + tBcB

π3M π2M minus tAcA minus tBcB

(11)

Considering the effect of subsidy on earnings based onthe AIGM we obtain the income range of the supplier inASM as shown in Figure 8

Using the same method of analysis in the AIGM weobtain the optimum decisions of the supplier and manu-facturers First we analyze whether the manufacturers willchoose to invest in advertising in ASM

Proposition 6 Manufacturers A and B choose to invest inadvertising in ASM

Proof When supplier M chooses not to label manufacturerBrsquos profits can be acquired by the Shapley value method asfollows

πN3B

16

PB + αBc(12)B1113872 1113873 minus 1 minus tB( 1113857cB (12)

Finding that manufacturer Brsquos profit is only related to itsinvestment and advertising investment can bring a positivenet income to manufacturer B is easy to understand +usmanufacturer B will choose to invest in advertising+en weanalyze manufacturer Arsquos investment decision and derive itsprofit as follows

πN3A

12

PA + αAc(12)A1113872 1113873 minus

13

PB + αBc(12)B1113872 1113873 minus 1 minus tA( 1113857cA

(13)

Under the premise that manufacturer B must invest inadvertising manufacturer A can derive positive net incomefrom advertising investment+erefore manufacturer A willalso invest in advertising

Similarly when supplier M chooses to label we have

πL3B

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873 minus 1 minus tB( 1113857cB (14)

πL3A 12

PA + αAc(12)A1113872 1113873 minus

13

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus 1 minus tA( 1113857cA

(15)

In the same way we can know that manufacturers A andB will invest in advertising when supplier M chooses to labelIn summary manufacturers A and B choose to invest inadvertising in ASM

We find that under the advertising subsidy mechanismthe manufacturers will still choose to invest in advertising Inaddition we can speculate that the manufacturers are morewilling to invest because the subsidy is harmless and ben-eficial to them +erefore the manufacturers may increaseinvestment under the advertising subsidy mechanism Nextwe will verify whether subsidy will promote the manufac-turersrsquo investment by analyzing the manufacturersrsquo optimalinvestment level and elucidate the optimal subsidy strategy

Proposition 7 Table 5 presents the optimal decisions ofplayers in ASM

Proof We can obtain the profit functions of the supplierunder different circumstances using the Shapley valuemethod When the supplier chooses not to label then

πN3M

12

PA + αAc(12)A1113872 1113873 +

16

PB + αBc(12)B1113872 1113873 minus tAcA minus tBcB

(16)

Otherwise

πL3M 12

PA + αAc(12)A1113872 1113873 +

16

PB + αB c0 + cB( 1113857(12)

1113872 1113873

minus tAcA minus tBcB minus c0

(17)

Based on equations (12)ndash(17) we can obtain the optimaldecisions of advertising investment and subsidy When Mchooses not to label we can derive cNlowastA α2A(16(1 minus tA)2)

and cNlowastB α2B(144(1 minus tB)2) from dπN3AdcA 0 and fromdπN

3BdcB 0 respectively +en we can obtain tNlowastA 13and tNlowastB 13 from zπN3MztA 0 and from zπN

3MztB 0respectively +erefore we have cNlowastA (964)α2A andcNlowastB (164)α2B

When supplier M opts to label we can derive cLlowastA

α2A(16(1 minus tA)2) and cLlowastB α2B(144(1 minus tB)2) minus c0 fromdπL

3AdcA 0 and from dπL3BdcB 0 respectively +en wehave tLlowastA 13 from zπL

3MztA 0 Based on zπL3MztB 0

we find that tLlowastB satisfies

α2B 1 minus 3tB( 1113857 + 144c0 1 minus tB( 11138573

0 (18)

Supplier M decideswhether to label

Supplier M decideswhether to grant subsidy

and how much to subsidize

Manufacturergoes into

production

Supplier and manufacturerdivide profit

Noncooperative stage Cooperative stage

Manufacturers decide whetherto invest in advertising and

how much to invest

Figure 7 Decision sequence of players in ASM

8 Complexity

Based on Equation (18) and cLlowastB α2B(144(1 minus tB)2) minus c0we have the following

tLlowastB 1 +

112

α2BK

minusK

c01113888 1113889

K 12c20α

2B +

144c40α4B + c30α6B1113969

1113874 1113875(13)

gt 0 (19)

cLlowastB

c0 3c0α2BK2 + K 12c20α2B minus K3( 1113857 minus c20α

2B α2B + 12K( 1113857( 1113857

K2 minus c0α2B( 11138572

(20)From Equation (18) and cLlowastB ge 0 we derive (3tLlowastB minus 1)

(2tLlowastB minus 1)le 0 as follows13le t

LlowastB le

12 (21)

First we analyze the optimal subsidy strategy of supplieraccording to Proposition 7 Longitudinally the subsidy formanufacturer B when supplier M chooses to label is higherthan that of the opposite Based on Proposition 4 manu-facturer B emerges with the ldquodiffusion of responsibilityrdquomindset in the face of the supplierrsquos decision to label+erefore supplier M will endowmanufacturer B with moresubsidies in an attempt to eliminate the mindset as much aspossible Horizontally when supplier M chooses to label thesubsidy to manufacturer B is higher than that to manu-facturer A because the supplier wants to improve his bar-gaining power in the negotiation with manufacturer A byclaiming to give more subsidies to manufacturer B

+en we analyze the optimal advertising investmentdecision of manufacturers When supplier chooses not tolabel the well-known manufacturer invests more than theweaker manufacturer to attract more attention from thesupplier +erefore the well-known manufacturer shouldalways retain its investment level to be higher than that of theweaker manufacturer to consolidate its market position Insummary supplier should endow the weaker manufacturerwith more subsidies when labeling and the well-knownmanufacturer should invest more than the weaker manu-facturer when supplier chooses not to label

Corollary 1 When supplier M chooses not to label anunderinvestment problem underlies the manufacturerrsquos ad-vertising investment In response subsidy can stimulate themanufacturersrsquo investment and mitigate the underinvestmentproblem

Proof By comparing the corresponding investment levels inTables 3 and 5 Corollary 1 can be proved For examplewhen supplier M chooses not to label manufacturer Arsquosoptimal investment levels in AIGM and ASM are (116)α2Aand (964)α2A as shown in Tables 3 and 5 respectively+erefore manufacturer Arsquos investment level in the AIGM isless than that in the ASM which reflects the un-derinvestment problem In addition subsidy can increasethe investment level of manufacturer A by (564)α2A

Corollary 1 confirms the existence of the un-derinvestment problem and shows that subsidy can stim-ulate manufacturersrsquo advertising investment level whichproves the importance of subsidy in coordinating the supplychain Finally we will further investigate the influence ofsubsidy on the supplier

Proposition 8 When the supplier chooses not to label thesubsidy strategy has a positive impact on the supplier suchthat the supplier will unconditionally issue subsidy to themanufacturers

Proof In the previous analysis we obtain the profits ofsupplier M when it does and does not grant subsidy If thesupplier chooses not to label then

πN3M minus πN2M

1576

9α2A + α2B1113872 1113873gt 0 (22)

We find that πN3M is always higher than πN2M which

indicates that the subsidy strategy has a positive impact onthe supplier who will unconditionally issue subsidy to themanufacturers when it opts not to label

In the ASM the advertising subsidy issued by thesupplier first promotes the investment of the manufacturersthat is the higher the investment the more improved thevalue of the products +is scenario thereby increases thebenefits of the cooperative alliance and ultimately improvesthe supplierrsquos profit+erefore the supplier should stimulatethe manufacturersrsquo investment by granting subsidies toincrease the intensity and promote the positive shift inequilibrium results of the competitive game so as to gainmore benefits in the next cooperative game In addition the

Supplier M

No label

Label

[PB + αBcB(12) ndash (1 + tB)cB PA + αAcA

(12) ndash (1 + tA)cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash (1 + tB)cB PA + αAcA(12) ndash c0 ndash (1 + tA)cA]

Figure 8 Income range of supplier in ASM

Table 5 Optimal decisions of players in ASM

SM clowastA clowastB tlowastA tlowastB

No label (964)α2A (164)α2B 13 13Label (964)α2A (α2B(144(1 minus tLlowastB )2)) minus c0 13 [13 12]

Complexity 9

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

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Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Based on Equation (18) and cLlowastB α2B(144(1 minus tB)2) minus c0we have the following

tLlowastB 1 +

112

α2BK

minusK

c01113888 1113889

K 12c20α

2B +

144c40α4B + c30α6B1113969

1113874 1113875(13)

gt 0 (19)

cLlowastB

c0 3c0α2BK2 + K 12c20α2B minus K3( 1113857 minus c20α

2B α2B + 12K( 1113857( 1113857

K2 minus c0α2B( 11138572

(20)From Equation (18) and cLlowastB ge 0 we derive (3tLlowastB minus 1)

(2tLlowastB minus 1)le 0 as follows13le t

LlowastB le

12 (21)

First we analyze the optimal subsidy strategy of supplieraccording to Proposition 7 Longitudinally the subsidy formanufacturer B when supplier M chooses to label is higherthan that of the opposite Based on Proposition 4 manu-facturer B emerges with the ldquodiffusion of responsibilityrdquomindset in the face of the supplierrsquos decision to label+erefore supplier M will endowmanufacturer B with moresubsidies in an attempt to eliminate the mindset as much aspossible Horizontally when supplier M chooses to label thesubsidy to manufacturer B is higher than that to manu-facturer A because the supplier wants to improve his bar-gaining power in the negotiation with manufacturer A byclaiming to give more subsidies to manufacturer B

+en we analyze the optimal advertising investmentdecision of manufacturers When supplier chooses not tolabel the well-known manufacturer invests more than theweaker manufacturer to attract more attention from thesupplier +erefore the well-known manufacturer shouldalways retain its investment level to be higher than that of theweaker manufacturer to consolidate its market position Insummary supplier should endow the weaker manufacturerwith more subsidies when labeling and the well-knownmanufacturer should invest more than the weaker manu-facturer when supplier chooses not to label

Corollary 1 When supplier M chooses not to label anunderinvestment problem underlies the manufacturerrsquos ad-vertising investment In response subsidy can stimulate themanufacturersrsquo investment and mitigate the underinvestmentproblem

Proof By comparing the corresponding investment levels inTables 3 and 5 Corollary 1 can be proved For examplewhen supplier M chooses not to label manufacturer Arsquosoptimal investment levels in AIGM and ASM are (116)α2Aand (964)α2A as shown in Tables 3 and 5 respectively+erefore manufacturer Arsquos investment level in the AIGM isless than that in the ASM which reflects the un-derinvestment problem In addition subsidy can increasethe investment level of manufacturer A by (564)α2A

Corollary 1 confirms the existence of the un-derinvestment problem and shows that subsidy can stim-ulate manufacturersrsquo advertising investment level whichproves the importance of subsidy in coordinating the supplychain Finally we will further investigate the influence ofsubsidy on the supplier

Proposition 8 When the supplier chooses not to label thesubsidy strategy has a positive impact on the supplier suchthat the supplier will unconditionally issue subsidy to themanufacturers

Proof In the previous analysis we obtain the profits ofsupplier M when it does and does not grant subsidy If thesupplier chooses not to label then

πN3M minus πN2M

1576

9α2A + α2B1113872 1113873gt 0 (22)

We find that πN3M is always higher than πN2M which

indicates that the subsidy strategy has a positive impact onthe supplier who will unconditionally issue subsidy to themanufacturers when it opts not to label

In the ASM the advertising subsidy issued by thesupplier first promotes the investment of the manufacturersthat is the higher the investment the more improved thevalue of the products +is scenario thereby increases thebenefits of the cooperative alliance and ultimately improvesthe supplierrsquos profit+erefore the supplier should stimulatethe manufacturersrsquo investment by granting subsidies toincrease the intensity and promote the positive shift inequilibrium results of the competitive game so as to gainmore benefits in the next cooperative game In addition the

Supplier M

No label

Label

[PB + αBcB(12) ndash (1 + tB)cB PA + αAcA

(12) ndash (1 + tA)cA]

[PB + αB(c0 + cB)(12) ndash c0 ndash (1 + tB)cB PA + αAcA(12) ndash c0 ndash (1 + tA)cA]

Figure 8 Income range of supplier in ASM

Table 5 Optimal decisions of players in ASM

SM clowastA clowastB tlowastA tlowastB

No label (964)α2A (164)α2B 13 13Label (964)α2A (α2B(144(1 minus tLlowastB )2)) minus c0 13 [13 12]

Complexity 9

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

supplier should give more subsidy to the weaker manu-facturer whereas the manufacturers should increase theirinvestment levels

Section 3 established the three models By comparing theBIGM with the AIGM we verified the existence of theldquodiffusion of responsibilityrdquo mindset Furthermore bycomparing the AIGM with the ASM we confirmed theunderinvestment problem and found that subsidy can al-leviate this problem In addition we noted that manufac-turer heterogeneity can lead to the differentiated subsidystrategies of the supplier Advertising subsidy can coordinatethe supply chain and achieve the Pareto improvement Wewill further study the supplierrsquos optimal decision and theimpact of subsidy by numerical analysis in response to thecomplexity of the analytical solution when the supplierchooses to label and grant subsidy

4 Numerical Analysis

To verify the validity of the model we carry out numericalanalysis at this juncture According to Assumptions (4) and(5) in Section 2 we set PA 2 PB 05 and αA αB 1πM and πM represent the supplierrsquos upper and lower profitbounds respectively

First we analyze the supplierrsquos decision to label in theBIGM Figure 9(a) depicts the relationship between labelingcost c0 and supplier Mrsquos profit π1M in the BIGM We findthat when the supplier chooses to label the upper profitbound decreases whereas the lower profit bound increaseswith the increase in labeling cost +erefore the profit in-terval of the supplierrsquos decision to label decreases with theincrease in labeling cost and is always smaller than that of thesupplierrsquos decision not to label Figure 9(b) is an enlargedimage of intersection πN

1M and πL1M in Figure 9(a) where we

find that πL1M gt πN1M when c0 lt 00277 +is finding indicates

that the supplier should choose labeling when labeling cost isrelatively low otherwise choose not labeling which confirmsProposition 1

Similarly we further explore the supplierrsquos optimaldecision when considering the manufacturersrsquo advertisinginvestment according to the relationship between labelingcost c0 and supplier Mrsquos profit π2M in the AIGM as shown inFigure 10 We find that the upper profit bound of thesupplierrsquos decision to label decreases with the increase inlabeling cost whereas the lower profit bound of the sup-plierrsquos decision to label coincides with that of the supplierrsquosdecision not to label +erefore the profit interval of thesupplierrsquos decision to label decreases with the increase inlabeling cost and is always smaller than that of supplierrsquosdecision not to label because of the existence of labeling costIn addition πN

2M is always higher than πL2M which indicates

that the profit of the supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore when considering advertising investment the suppliershould always opt not to label to maximize profits whichverifies Proposition 5 In addition we find that πN

2M gt πN1M bycomparing Figure 9 with Figure 10 which indicates that theequilibrium strategy of advertising investment can increasethe supplierrsquos profit

Next we shed light on supplier Mrsquos profit in the ASMFigure 11 displays the relationship between labeling cost c0and supplier Mrsquos profit π3M We find that when the supplierchooses to label its upper profit bound decreases whereas itslower profit bound increases with the increase in labelingcost +erefore the profit interval of the supplierrsquos decisionto label decreases with the increase in labeling cost and isalways smaller than that of the supplierrsquos decision not tolabel

Observation 1 +e supplier should always choose not tolabel in the ASM

We find that πN3M gt πL3M from Figure 11 which indicates

that the profit of supplierrsquos decision not to label is alwaysgreater than that of the supplierrsquos decision to label +ere-fore the supplier should always choose not to label in theASM to maximize profits

Based on Observation 1 we find that πN3M is slightlyhigher than πN

2M by comparing Figure 10 with Figure 11which indicates that subsidy can increase the benefits of thesupplier +erefore the supplier should grant subsidies tothe manufacturers to maximize its profits which confirmsProposition 8 In summary the supplier should choose notto label and grant subsidy in the ASM

Figures 9ndash11 discuss the optimal decision of the supplierin the BIGM AIGM and ASM respectively In summarythe supplier should choose to label when labeling cost isrelatively low without considering advertising investmentand should always choose not to label when consideringadvertising investment No labeling and granting subsidy arethe supplierrsquos optimal strategy in the advertising subsidymechanism

On the basis of these conclusions we further discuss theimpact of subsidy on the supplier under different values ofthe investment return coefficient αi As shown inFigure 12(a) πN3M minus πN

2M is used to indicate the impact ofsubsidy on the supplierrsquos profits Figure 12(b) presents acorresponding contour map We find that πN

3M minus πN2M gt 0

which increases continuously with the increases in αA andαB indicates that subsidy has a sustained positive effect onthe supplier In other words the greater the ability to earnreturns from investment the more profit increment thesubsidy can bring to the supplier In addition αA has amore significant impact on profit increment compared withαB which indicates that manufacturer heterogeneity mayenable the supplier to obtain different degrees of benefitsfrom the subsidy mechanism Manufacturer A is a well-known enterprise with good reputation whereas manu-facturer B is a weaker enterprise which may result in agreater impact on A compared with B in terms of subsidydue to the different investment returns abilities +ereforethe supplier should not only decide the optimal subsidy ratebut also evaluate the investment returns ability of themanufacturers and pay more attention to that of the well-known manufacturer

Moreover we will discuss the impact of subsidy onmanufacturer A Figure 13 displays the relationship betweenπ3A minus π2A and αA Horizontally profit margin increases withthe increase in αA If the supplier decides not to label then

10 Complexity

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

subsidy will exert a positive effect on manufacturer Arsquosprofit when αA gt 0666 If the supplier decides to label thensubsidy will have a positive effect only when αA gt 0189+is finding indicates that when M chooses to labelmanufacturer A will be required to display an increasedefficiency in advertising investment In other wordsmanufacturer A should improve its investment profit-ability to ensure the possibility for cooperation withsupplier M Longitudinally manufacturer Arsquos profitmargin is always higher when the supplier decides not tolabel compared with when the supplier decides to label+is finding indicates that the supplierrsquos decision not tolabel can bring added benefits not only to itself but also tomanufacturer A

Finally we discuss the impact of subsidy on manufac-turer B Figure 14 depicts the relationship between π3B minus π2B

and αB Horizontally the profit margin increases with theincrease in αB When the supplier decides not to labelπN3B minus πN2B gt 0 subsidy will exert a continuous positive effect

on manufacturer Brsquos profits When the supplier decides tolabel πL3B minus πL

2B lt 0 subsidy will exert a continuous negativeeffect on manufacturer Brsquos profits Longitudinally manu-facturer Brsquos profit margin is always higher when the supplierdecides not to label than that when the supplier decides tolabel In summary subsidy can benefit the weaker manu-facturer only under the supplierrsquos optimal decision that isnot to label

We refer to Figures 12ndash14 and find that the advertisingsubsidy mechanism can enhance the profit of each supplychain member under the optimal strategy set thus co-ordinating the organic food supply chain and achieving thePareto improvement

0 002 00400277

006 008

πndashN1M

πndashL1M

πL1M

πndash1

LM

π1ndashN

M

π1NM

01 012 014 016 018 0204

06

08

1

12

14

16

18

2

22

c0

π 1M

(a)

πL1M π1

NM

0 0005 001 0015 002 0025 003c0

π 1M

0035 004 0045 005

09

095

1

105

11

115

12

125

13

00277

(b)

Figure 9 Relationship between c0 and π1M (a) supplierrsquos profits (b) enlarged image of inset in (a)

040 002

π 2M

004 006 008c0

01 012 014 016 018 02

06

08

1

12

14

16

18

2

22

24

πndash2

NM

πndash2

LM

π2LM

π2NM

πNndash2M = πL

ndash2M

Figure 10 Relationship between c0 and π2M

πndashN3M

πndashL3M

π3NM

π3LM

πndash3

LM

πndash3

NM

04

06

08

1

12

14

16

18

2

22

24π 3

M

0 002 004 006 008 01 012 014 016 018 02c0

Figure 11 Relationship between c0 and π3M

Complexity 11

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

5 Conclusions and Managerial Insights

In the face of consumersrsquo preference for organic food and thegovernmentrsquos low-carbon policy we establish a tripartitegame model to study the decisions of labeling and adver-tising investment in an organic food supply chain composedof one supplier and two heterogeneous manufacturers by thebiform game approach In addition we introduced an ad-vertising subsidy mechanism to alleviate the un-derinvestment problem and coordinate the supply chainFirst this study established the BIGM to investigate thesupplierrsquos labeling decision without considering advertisinginvestment +en we build the AIGM to further elucidatethe impact of the manufacturersrsquo advertising investment onthe supplierrsquos labeling decision and obtain the optimalstrategies of the supply chain members Finally we in-troduced a coordination mechanism namely ASM to al-leviate the underinvestment problem and coordinate the

supply chain and presented the optimal strategies of thesupply chain members in the ASM As a result we obtainedinteresting findings with managerial insights

Without considering advertising investment the sup-plierrsquos decision to label is dependent on labeling cost +esupplier should opt to label when labeling cost is relativelylow to achieve higher profit When labeling cost becomeshigh labeling investment will enter the stage of diminishingreturns to scale which will adversely affect the supplierrsquosprofits At this time the supplier should decide not to labelIn addition the cooperative game in this model is super-additive which indicates that each supply chain member iswilling to cooperate because the total benefit from co-operation is always no less than the sum of the income fromtheir respective operations

Taking advertising investment into account all manu-facturers should invest in advertising to improve

αA

αB

004

003

002

001

015

π 3N M ndash

π2N M

151

1

05 05

(a)

000

5

001

001

001

5

001

5

002

002

002

50

025

003

003

003

50

035

0505 06 07

αA

α B

08 09 1 11 12 13 14 15

06

07

08

09

1

11

12

13

14

15

(b)

Figure 12 Impact of subsidy on supplier (a) profit increment of supplier (b) contour map

ndash00405 06 07 08 09

0666 01891 11 12 13 14 15

ndash003

ndash002

ndash001

0

001

002

003

004

005

006

αA

π3NA ndash π2

NA

π3LA ndash π2

LA

π 3A

ndash π

2A

Figure 13 Impact of subsidy on manufacturer A

ndash007

ndash006

ndash005

ndash004

ndash003

ndash002

ndash001

0

001

05 06 07 08 09 1 11 12 13 14 15αB

π 3B ndash

π2B

π3NB ndash π2

NB

π3LB ndash π2

LB

Figure 14 Impact of subsidy on manufacturer B

12 Complexity

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

competitiveness which is the result of dominant equilib-rium When the supplier decides to label the weakermanufacturer should reduce its investment in advertisingappropriately whereas the well-knownmanufacturer shouldmaintain its investment level at a higher level than that of theweaker manufacturer to consolidate its market position andcompetitiveness In the face of the manufacturersrsquo in-vestment the supplier should decide not to label so as toprevent advertising investment from entering the stage ofdiminishing returns to scale

When considering advertising investment and subsidythe manufacturers will invest more in advertising whichconfirms the existence of underinvestment and indicates thepromotion effect of subsidy on advertising investment+erefore the supplier should subsidize the manufacturersto stimulate investment and subsidize the weaker manu-facturer more to weaken the ldquodiffusion of responsibilityrdquomindset and gain increased bargaining power with the well-known manufacturer Using the subsidy mechanism tomitigate the underinvestment problem encourages themanufacturersrsquo investment to move toward the optimalequilibrium point As a result the profit of the cooperativealliance will tend to peak such that the supplier may nolonger need to label

By a comparative analysis of the AIGM and BIGM wefind a relationship between competitive game and co-operative game First two heterogeneous manufacturersinvest in advertising through competitive game and obtainthe equilibrium result of competitive game which improvesthe supplierrsquos advantage in the next cooperative game +isscenario does not necessitate the supplier to label thuspromoting a positive shift in the equilibrium result of thecooperative game Furthermore by a comparative analysis ofthe AIGM and ASM we identify the transmission mecha-nism of advertising subsidy +e supplier can stimulate themanufacturersrsquo investment by issuing subsidies to increasethe intensity of the competitive game and promote a positivemovement in the equilibrium result of the competitive gameand obtain more benefits in the cooperative game More-over we find an interesting phenomenon on cooperationand investment in the organic food supply chain that is theldquodiffusion of responsibilityrdquo mindset may exist in the face ofthe investment behavior of the other side which will lead tothe phenomenon of underinvestment (eg manufacturer Bdecreases its advertising investment level according to thelabeling behavior of supplier M in the AIGM) or even thephenomenon of noninvestment (eg supplier M decides notto label with the manufacturersrsquo advertising investment)

Although this study garnered several important mana-gerial implications we acknowledge certain limitations thatcan be addressed in future studies By summarizing optimaldecisions in the AIGM and ASM we find that the supplierwho makes the decision first always chooses not to labelwhereas two manufacturers always choose to invest in ad-vertising In other words the supplier can make less effortcompared with the manufacturers in a cooperative alliancewhich indicates that the decision-making sequence gives thesupplier the ldquofirst-mover advantagerdquo in the cooperativegame In the future the research direction will focus on the

optimal strategy when manufacturers make the first de-cision In addition although this study introduced the ad-vertising subsidy mechanism to coordinate the supply chainthis subsidy belongs to one-way subsidy +erefore whetheror not two-way subsidy is superior over one-way subsidy inorganic food supply chains with advertising investment andlabeling is also one of the topics that we will discuss in thefuture

Data Availability

No data were used to support this study

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Humanities and SocialSciences Research Programs ofMinistry of Education China(no 17YJC630097)

References

[1] H Huang J Zhang X Ren and X Zhou ldquoGreenness andpricing decisions of cooperative supply chains consideringaltruistic preferencesrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 1 p 51 2018

[2] Y Ozinci Y Perlman and S Westrich ldquoCompetition be-tween organic and conventional products with differentutilities and shelf livesrdquo International Journal of ProductionEconomics vol 191 pp 74ndash84 2017

[3] Y Wang Y Wang and Y Zhu ldquoWhat could encouragefarmers to choose non-chemical pest management Evidencefrom apple growers on the Loess Plateau of Chinardquo CropProtection vol 114 pp 53ndash59 2018

[4] Q Hu and B Xu ldquoDifferential game analysis of optimalstrategies and cooperation in omni-channel organic agri-cultural supply chainrdquo Sustainability vol 11 no 3 p 8482019

[5] S Longo M Mistretta F Guarino and M Cellura ldquoLifeCycle Assessment of organic and conventional apple supplychains in the North of Italyrdquo Journal of Cleaner Productionvol 140 pp 654ndash663 2017

[6] J P Reganold and J M Wachter ldquoOrganic agriculture in thetwenty-first centuryrdquo Nature Plants vol 2 no 2 8 pages2016

[7] L M Vieira and A Hoppe ldquoOrganic food production andcontrolrdquo Encyclopedia of Food and Health pp 178ndash180 2016

[8] J Rana and J Paul ldquoConsumer behavior and purchase in-tention for organic food a review and research agendardquoJournal of Retailing and Consumer Services vol 38 pp 157ndash165 2017

[9] C R R Pleguezuelo V H D Zuazo J R F MartınezF J M Peinado F M Martın and I F G Tejero ldquoOrganicolive farming in Andalusia Spain A reviewrdquo Agronomy forSustainable Development vol 38 no 2 p 16 2018

[10] V Seufert N Ramankutty and J A Foley ldquoComparing theyields of organic and conventional agriculturerdquo Naturevol 485 no 7397 pp 229ndash232 2012

[11] X Gao and H Zheng ldquoEnvironmental concerns environ-mental policy and green investmentrdquo International Journal of

Complexity 13

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Environmental Research and Public Health vol 14 p 15702017

[12] E Feess and J-H +un ldquoSurplus division and investmentincentives in supply chains a biform-game analysisrdquo Euro-pean Journal of Operational Research vol 234 no 3pp 763ndash773 2014

[13] A Brandenburger and H Stuart ldquoBiform gamesrdquo Manage-ment Science vol 53 no 4 pp 537ndash549 2007

[14] E Kemahlıoglu-Ziya and J J Bartholdi III ldquoCentralizinginventory in supply chains by using Shapley value to allocatethe profitsrdquo Manufacturing amp Service Operations Manage-ment vol 13 no 2 pp 146ndash162 2011

[15] F Liu W-L Chen and D-B Fang ldquoOptimal coordinationstrategy of dynamic supply chain based on cooperative sto-chastic differential game model under uncertain conditionsrdquoApplied Soft Computing vol 56 pp 669ndash683 2017

[16] J Gao X Yang and D Liu ldquoUncertain Shapley value ofcoalitional game with application to supply chain alliancerdquoApplied Soft Computing vol 56 pp 551ndash556 2017

[17] Z Xu Z Peng L Yang and X Chen ldquoAn improved Shapleyvalue method for a green supply chain income distributionmechanismrdquo International Journal of Environmental Researchand Public Health vol 15 no 9 p 1976 2018

[18] M A Miranda-Ackerman and C Azzaro-Pantel ldquoExtendingthe scope of eco-labelling in the food industry to drive changebeyond sustainable agriculture practicesrdquo Journal of Envi-ronmental Management vol 204 pp 814ndash824 2017

[19] B Ellison B R L Duff Z Wang and T B White ldquoPuttingthe organic label in context examining the interactions be-tween the organic label product type and retail outletrdquo FoodQuality and Preference vol 49 pp 140ndash150 2016

[20] N Loebnitz and J Aschemann-Witzel ldquoCommunicatingorganic food quality in China consumer perceptions of or-ganic products and the effect of environmental value prim-ingrdquo Food Quality and Preference vol 50 pp 102ndash108 2016

[21] Y Yu X Han and G Hu ldquoOptimal production for manu-facturers considering consumer environmental awareness andgreen subsidiesrdquo International Journal of Production Eco-nomics vol 182 pp 397ndash408 2016

[22] C DrsquoSouza and E Yiridoe ldquoProducerrsquos self-declared windenergy ECO-labeling consequences on the market a Cana-dian case studyrdquo Sustainability vol 11 no 5 1218 pages2019

[23] J Song F Li D DWu L Liang and A Dolgui ldquoSupply chaincoordination through integration of innovation effort andadvertising supportrdquo Applied Mathematical Modellingvol 49 pp 108ndash123 2017

[24] S Karray and S H Amin ldquoCooperative advertising in asupply chain with retail competitionrdquo International Journal ofProduction Research vol 53 no 1 pp 88ndash105 2014

[25] B Liu G G Cai and A A Tsay ldquoAdvertising in asymmetriccompeting supply chainsrdquo Production and OperationsManagement vol 23 no 11 pp 1845ndash1858 2014

[26] X Hong L Xu P Du and W Wang ldquoJoint advertisingpricing and collection decisions in a closed-loop supplychainrdquo International Journal of Production Economicsvol 167 pp 12ndash22 2015

[27] T-H Chen ldquoEffects of the pricing and cooperative advertisingpolicies in a two-echelon dual-channel supply chainrdquo Com-puters amp Industrial Engineering vol 87 pp 250ndash259 2015

[28] Z Wu L Feng and D Chen ldquoCoordinating pricing andadvertising decisions for supply chain under consignmentcontract in the dynamic settingrdquo Complexity vol 2018 Ar-ticle ID 7697180 11 pages 2018

[29] Q Gou Y-W Zhang L Liang Z Huang and A AshleyldquoHorizontal cooperative programmes and cooperative ad-vertisingrdquo International Journal of Production Researchvol 52 no 3 pp 691ndash712 2014

[30] Z Guo and J Ma ldquoDynamics and implications on a co-operative advertising model in the supply chainrdquo Commu-nications in Nonlinear Science Numerical Simulation vol 64pp 198ndash212 2018

[31] F LuW Tang G Liu and J Zhang ldquoCooperative advertisinga way escaping from the prisonerrsquos dilemma in a supply chainwith sticky pricerdquo Omega vol 86 pp 87ndash106 2019

[32] P De Giovanni S Karray and G Martın-Herran ldquoVendorManagement Inventory with consignment contracts and thebenefits of cooperative advertisingrdquo European Journal ofOperational Research vol 272 no 2 pp 465ndash480 2019

[33] D Xiao Y-W Zhou Y Zhong and W Xie ldquoOptimal co-operative advertising and ordering policies for a two-echelonsupply chainrdquo Computers amp Industrial Engineering vol 127pp 511ndash519 2019

[34] T Chernonog and T Avinadav ldquoPricing and advertising in asupply chain of perishable products under asymmetric in-formationrdquo International Journal of Production Economicsvol 209 pp 249ndash264 2019

[35] X Li Y Li and W Cao ldquoCooperative advertising models inO2O supply chainsrdquo International Journal of ProductionEconomics vol 215 pp 144ndash152 2019

[36] M Proch K Worthmann and J Schluchtermann ldquoA ne-gotiation-based algorithm to coordinate supplier develop-ment in decentralized supply chainsrdquo European Journal ofOperational Research vol 256 no 2 pp 412ndash429 2017

[37] S Alaei andM Setak ldquoSupply chain coordination via two-waycooperative advertising contract considering competing re-tailersrdquo Scientia Iranica vol 23 no 5 pp 2330ndash2340 2016

[38] X Chen Z Luo and X Wang ldquoCompete or cooperate in-tensity dynamics and optimal strategiesrdquo Omega vol 86pp 76ndash86 2019

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom