Research Article Research on Cooperation Strategy of Enterprises ...downloads.hindawi.com/journals/ddns/2015/301245.pdf · Enterprise A Noncooperation Enterprise A Enterprise A Semicooperation

Research ArticleResearch on Cooperation Strategy of Enterprises’ Quality andSafety in Food Supply Chain

Jining Wang, Tingqiang Chen, and Junyong Wang

School of Economic and Management, Nanjing Tech University, Nanjing 211816, China

Correspondence should be addressed to Tingqiang Chen; [email protected] and Junyong Wang; [email protected]

Received 21 July 2015; Accepted 25 August 2015

Academic Editor: Paolo Renna

Copyright © 2015 Jining Wang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In order to prevent and control risk factors which harm the quality and safety of the food supply chain effectively and reduce theprobability of food safety incidents, this paper investigated on some problems of the upstream and downstream enterprises of thefood supply chain under the three different forms of cooperation based on the neoclassic economics and game theory method.These problems include the effectiveness of the quality and safety efforts, the profits, the effect of the losses that the food safetyincidents caused on the quality efforts’ efficacy, and the social welfare comparison. Meanwhile, we constructed evolutionary gamemodel to analyze the macro and micro factors that influenced the cooperation strategy and demonstrated the effect of diversity ofdecision-making parameters on evolution results based on numerical simulation. By the theoretical and simulation analysis, wefound that (1) the quality efforts’ efficacy, the profits, the sensitivity coefficient of the quality efforts efficiency to the losses, and thesocial welfare without thinking about the externality all met their maximum under the full cooperation situation; (2) strengtheningsupervision over the source of the food supply chain can reduce the probability of food safety incidents; (3) macro and microenvironment will be the important basis for companies’ decision-making on cooperation strategy in the food supply chain.

1. Introduction

Food safety is related to the life andhealth of thewhole nation,the healthy development of the economy, social harmony andstability, and the image of state and government.However, thefood safety incidents thatmany factors caused have happenedfrequently in recent years. These factors included the foodmarkets failures due to the food markets’ externality and“lemon market effect” that information asymmetry in foodmarkets caused [1–3], themismatch between the costs and thebenefits made the center of interest gravity shift toward thedownstream of the industry, food companies paid too muchattention to the market share and put the risks which wereaccumulated by the upstream interests contradiction to theextreme through the transmission of leverage effect, and soforth [4, 5].The frequent occurrences of food safety accidentshave led to consumers’ extreme lack of social trust in foodsafety andweakened consumers’ willingness to spend on food[6] and numerous consumers have been in a state of panic.

Risk factors of food safety throughout each link of thewhole supply chain are from the source’s supply of raw mate-rials, the cultivation and breeding of agricultural products,

the production and processing, and logistics distribution toretail terminal. Risk factors existing in each link (e.g., abuseof pesticides in the planting and breeding links and use offood additives excessively in the production and processinglinks) would pass on the food supply chain, and then itproduced the agglomeration and amplification effects and ledto the occurrence of food safety incidents eventually [7–12].Therefore, it is not only the tasks of one side or an enterprise,but the responsibility of all the main participant bodies in thefood supply chain to ensure the food safety.

Many factors, for example, information asymmetry [13–16] and the interest game imbalance between all the mainparticipant bodies in the food supply chain [17], could inducethe occurrence of the “adverse selection” and “moral hazard”behavior which harmed the food safety.The adverse selectionproblems in the food supply chain could be solved effectivelyby way of investigating the main participant bodies’ pastperformance and business reputation and the main partic-ipant bodies to adopting a third-party certification, estab-lishing long-term strategic cooperative partnership betweenthe main participant bodies, transforming the enterprise’s

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2015, Article ID 301245, 15 pageshttp://dx.doi.org/10.1155/2015/301245

2 Discrete Dynamics in Nature and Society

business philosophy, and so forth [18–20]. The moral hazardproblems in the food supply chain could be solved effectivelyby way of establishing the appropriate incentive and supervi-sionmechanism [21–24]. From the perspective of food supplychain, it could realize the goal of enhancing the food supplychain’s ability to effectively resist and control food safety riskthrough establishing synergy mechanism among all the mainparticipants [25–31]. However, the literatures [25–31] just putforward a thinking framework and lack of concrete and in-depth research on the synergy strategies between the mainparticipant bodies in the food supply chain.

It is exactly based on the above consideration that thispaper tries from the aspect of food supply chain to realizeclose cooperation between all of the links (the node enter-prises) in the food supply chain through establishing thecooperation, incentive, and supervision mechanism and toreach the goals for preventing and controlling risk factorswhich harm the quality and safety of the food supply chaineffectively and reducing the probability of food safety inci-dents. This paper is structured as follows. Section 2 presentssome assumptions, defines the notation used in this paper,presents the profit function models of enterprises in the foodsupply chain, and discusses the profit function models ofenterprises in the food supply chain. Section 3 highlights theeffects of the macro and micro factors on the enterprises’collaboration strategy for the quality and safety throughnumerical simulations.The final section contains concludingremarks.

2. The Design of Cooperation, Incentive, andSupervision Contract Constraint Mechanism

2.1. The Establishment of the Theoretical Model

Assumption 1. This paper analyzes the problems about qualityand safety cooperation between the upstream enterprise 𝐴and the downstream enterprise 𝐵 from the perspective offood supply chain. Enterprise 𝐵 is the retail terminal thathas a certain processing capability relative to the enterprise𝐴. Meanwhile both enterprises 𝐴 and 𝐵 are regulated by thegovernmental supervision department’s quality and safety.

Assumption 2. Both enterprises 𝐴 and 𝐵 put the qualityefforts as decision variables and make a choice betweenquality efforts cooperation and noncooperation in order toachieve the double-edged optimization goals, which are thefood security and the profit maximization.

Assumption 3. The effectiveness of the quality efforts, theprofits, and the social welfare of both enterprises 𝐴 and 𝐵are all different under the different cooperation modalities.The quality efforts’ efficacy of enterprise 𝐴 will have certainimpact on enterprise 𝐵, and vice versa.

Assumption 4. There is no comparison between the extents ofthe different food commodities’ quality efforts. However, thequality effort efficiency (the probability of food safety inci-dents) can be compared in the different food commodities.

Assumption 5. Products of enterprises 𝐴 and 𝐵 belong to thenecessities. The market is the imperfect competition market.And the demand for food is a linear function of food price.Meanwhile, food inventories of both enterprises 𝐴 and 𝐵 arezero.

Assumption 6. The unit food quality effort (the amount ofper unit food quality and safety events that can be reduced)is constant under certain conditions. And the total qualityefforts of both enterprises𝐴 and𝐵 are linear functions of foodproduction.

Assumption 7. The quality effort cost is a monotone increas-ing function of the quality effort efficiency, and the marginalcost of quality effort increases with the increasing of thequality effort efficiency. The inputs on quality efforts have noimpact on the food production cost.

Assumption 8. The average number of quality and safetyevents of per unit food of both enterprises𝐴 and 𝐵 is𝑁

𝐴,𝑁𝐵

in one year.The loss that the average quality and safety eventsof per unit food caused each time is 𝑆. The average number ofquality and safety events of the unit food of both enterprises𝐴and𝐵 that can be reduced in one year isΔ𝑁

𝐴,Δ𝑁𝐵for quality

effort. The quality effort efficiency of enterprise is 𝑓𝑖=𝐴,𝐵

, and0 ≤ 𝑓

𝑖= Δ𝑁

𝑖/𝑁𝑖(𝑖 = 𝐴, 𝐵) < 1. The retail price of food is

𝑝, the demand for food is 𝑄, the total quality efforts of bothenterprises 𝐴 and 𝐵 are 𝐸

𝑖(𝑄), and 𝐸

𝑖(𝑄) = Δ𝑁

𝑖𝑄. The total

quality efforts costs of both enterprises 𝐴 and 𝐵 are 𝐶(𝑓𝑖),

which satisfies 𝜕𝐶(𝑓𝑖)/𝜕𝑓𝑖> 0, 𝜕2𝐶(𝑓

𝑖)/𝜕𝑓𝑖

2> 0, 𝐶(0) = 0,

and 𝐶(1) = +∞. In general, we can assume that 𝐶(𝑓𝑖) is the

quadratic function of the quality effort efficiency according tothe literatures [15, 16], which satisfies 𝐶(𝑓

𝑖) = (1/2)𝑛𝑓

𝑖

2, and𝑛 is on behalf of the extent of the quality effort. It is indicatedthat the greater the 𝑛 is, the higher the quality effort cost is.The production cost of per unit food is 𝑐

𝑖, and the wholesale

price of food is 𝑐𝑝.

We can construct the profit function of enterprise𝐴 basedon the above assumptions, which satisfies 𝐿

𝐴= [𝑐𝑝− 𝑐𝐴−

𝑁𝐴𝑆(1 − 𝑓

𝐴)]𝑄 − (1/2)𝑛𝑓

2

𝐴, and assume that the market

demand for high-quality food satisfies 𝑄 = 𝑁 − 𝑎𝑝, 𝑁 onbehalf of market capacity and 𝑎 on behalf of the sensitivitycoefficient of demand price. Thus the profit function ofenterprise 𝐴 can be represented as follows:

𝐿𝐴= [𝑐𝑝− 𝑐𝐴− 𝑁𝐴𝑆 (1 − 𝑓

𝐴)] (𝑁 − 𝑎𝑝) −

1

2𝑛𝑓2

𝐴. (1)

In the same way, the profit function of enterprise 𝐵 can berepresented as follows:

𝐿𝐵= [𝑝 − 𝑐

𝑝− 𝑐𝐵− 𝑁𝐵𝑆 (1 − 𝑓

𝐵)] (𝑁 − 𝑎𝑝) −

1

2𝑛𝑓2

𝐵. (2)

The game between enterprises𝐴 and𝐵 is divided into twostages. The first stage is about the level of quality effort; thesecond stage is about the food price. The two-stage game can

Discrete Dynamics in Nature and Society 3

Enterprise A

Noncooperation

Enterprise A

Enterprise A

Semicooperation

Cooperation

Enterprise B

Enterprise B

Enterprise B

fi=A,B fi=A,B

fi=A,B

fi=A,B

cp

cp

p

p

p

Figure 1: The game process of three forms.

be divided into three forms (as shown in Figure 1) accordingto the different forms of cooperation between enterprises, asfollows.

The First Form. Noncooperation, namely, NC, means thatboth enterprises 𝐴 and 𝐵 are uncooperative in the quality,safety, and price. The food price of enterprise 𝐵 needs tobe determined based on the wholesale price of enterprise𝐴, and the basis of their decision-making is based on profitmaximization.

The Second Form. Semicooperation, namely, BC, means thatboth enterprises 𝐴 and 𝐵 are just cooperative in the qualityand safety, and the profit maximization is the basis of theirfood price decision-making. However, the goal to maximizethe profits of the entire food supply chain is the basis of theirquality efforts investment decision-making.

The Third Form. Cooperation, namely, HC, means that thecomplete trust working relationship between enterprises 𝐴and 𝐵 has been established. The goal to maximize the profitsof the entire food supply chain is the basis of their retail priceof food and quality efforts investment decision-making, but𝑐𝑝does not exist at the moment.Let us solve the above problems based on the backward

induction.

(1)The First Form:The Form of Noncooperation.The food saleprice decision-making of enterprise 𝐵 is based on the profitmaximization under the situation of noncooperation.

Proposition 9. The downstream enterprise’s quality effortsefficiency is lower than the upstream enterprise when𝑁

𝐴= 𝑁𝐵

under the situation of noncooperation.

Demonstration. Let 𝜕𝐿𝐵/𝜕𝑝 = (𝑁 − 𝑎𝑝) − 𝑎[𝑝 − 𝑐

𝑝− 𝑐𝐵−

𝑁𝐵𝑆(1 − 𝑓

𝐵)] = 0; thus 𝑝∗NC and 𝑄∗NC can be obtained; bring

them into (1), and let 𝜕𝐿𝐴/𝜕𝑐𝑝= 0; thus 𝑐∗

𝑝NC, 𝑝∗

NC, and 𝑄∗

NCcan be obtained, as follows:

𝑐∗

𝑝NC

=𝑁 + 𝑎 [𝑐

𝐴− 𝑐𝐵+ 𝑁𝐴𝑆 (1 − 𝑓

𝐴) − 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]

2𝑎

𝑝∗

NC

=3𝑁 + 𝑎 [𝑐

𝐴+ 𝑐𝐵+ 𝑁𝐴𝑆 (1 − 𝑓

𝐴) + 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]

4𝑎,

𝑄∗

NC

=𝑁 − 𝑎 [𝑐


𝐴) + 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]

4.

(3)

Bring 𝑄∗NC into (1) and (2); due to 𝜕𝐿𝐴/𝜕𝑓𝐴

< 0,𝜕𝐿𝐵/𝜕𝑓𝐵< 0; thus, letting 𝜕𝐿

𝐴/𝜕𝑓𝐴= 0, 𝜕𝐿

𝐵/𝜕𝑓𝐵= 0, 𝑓

𝐴,

𝑓𝐵can be obtained, as follows:

𝑓𝐴=𝑁𝐴𝑆 {𝑁 − 𝑎 [𝑐

𝐴+ 𝑐𝐵+ 𝑁𝐴𝑆 + 𝑁

𝐵𝑆 (1 − 𝑓

𝐵)]}

4𝑛 − 𝑎𝑁2

𝐴𝑆2

,

𝑓𝐵=𝑁𝐵𝑆 {𝑁 − 𝑎 [𝑐

𝐴+ 𝑐𝐵+ 𝑁𝐵𝑆 + 𝑁

𝐴𝑆 (1 − 𝑓

𝐴)]}

8𝑛 − 𝑎𝑁2

𝐵𝑆2

.

(4)

With (4), the optimal values of quality efforts efficiency ofboth enterprises 𝐴 and 𝐵 can be obtained, as follows:

𝑓∗

𝐴NC =2𝑁𝐴𝑆 [𝑁 − 𝑎 (𝑐


𝐵𝑆)]

8𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 2𝑁2

𝐴)

,

𝑓∗

𝐵NC =𝑁𝐵𝑆 [𝑁 − 𝑎 (𝑐


𝐵𝑆)]

8𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 2𝑁2

𝐴)

.

(5)

Therefore, 𝑓∗𝐴NC = 𝑓

∗

𝐵NC when 𝑁𝐴= 𝑁𝐵. Proposition 9

has been demonstrated to be correct.


(2) The Second Form: The Form of Semicooperation. Qualityefforts investment decision-making is made by both enter-prises 𝐴 and 𝐵 under the situation of semicooperation. Butthe food price decision-making is, respectively, made bythemselves; namely, the game of the second stage is the sameas the situation of noncooperation; meanwhile, the equationthat 𝑐∗

𝑝BC = 𝑐∗

𝑝NC, 𝑝∗

BC = 𝑝∗

NC, and 𝑄∗

BC = 𝑄∗

NC can beobtained.

Proposition 10. There exists local maximum in the overallprofits of the food supply chain under the situation of semi-cooperation, and the downstream enterprise’s quality effortsefficiency is equal to the upstream enterprise when𝑁

𝐴= 𝑁𝐵.

Demonstration. Quality efforts investment decision-makingwill be made by both enterprises 𝐴 and 𝐵 in order to achievethe goal that maximizes the overall profits of the food supplychain of the first stage.The profit functions of enterprises andthe whole food supply chain at the moment are the following:

𝐿𝐴BC

={𝑁 − 𝑎 [𝑐


𝐴) + 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]}2

8𝑎

−1

2𝑛𝑓2

𝐴

𝐿𝐵BC

={𝑁 − 𝑎 [𝑐


𝐴) + 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]}2

16𝑎

−1

2𝑛𝑓2

𝐵

𝐿BC

=3 {𝑁 − 𝑎 [𝑐


𝐴) + 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]}2

16𝑎

−1

2𝑛 (𝑓2

𝐴+ 𝑓2

𝐵) .

(6)

Thus that Hessian Matrix can be obtained:

𝐻BC = (

𝜕2𝐿BC𝜕𝑓2

𝐴

𝜕2𝐿BC

𝜕𝑓𝐴𝜕𝑓𝐵

𝜕2𝐿BC

𝜕𝑓𝐵𝜕𝑓𝐴

𝜕2Ω

𝜕𝑓2

𝐵

)

=(

3𝑎𝑁2

𝐴𝑆2

8− 𝑛

3𝑎𝑁𝐴𝑁𝐵𝑆2

8

3𝑎𝑁𝐴𝑁𝐵𝑆2

8

3𝑎𝑁2

𝐵𝑆2

8− 𝑛

) .

(7)

Consider |𝐻BC| = 𝑛[𝑛 − 3𝑎𝑆2(𝑁2

𝐴+ 𝑁2

𝐵)/8] > 0. Therefore,

there exists local maximum in the overall profits of the foodsupply chain. Let 𝜕𝐿BC/𝜕𝑓𝐴 = 0, 𝜕𝐿BC/𝜕𝑓𝐵 = 0; thus theoptimal values of quality efforts efficiency of both enterprises

𝐴 and 𝐵 can be obtained by solving the simultaneous equa-tions, as follows:

𝑓∗

𝐴BC =3𝑁𝐴𝑆 [𝑁 − 𝑎 (𝑐


𝐵𝑆)]

8𝑛 − 3𝑎𝑆2 (𝑁2

𝐵+ 𝑁2

𝐴)

,

𝑓∗

𝐵BC =3𝑁𝐵𝑆 [𝑁 − 𝑎 (𝑐


𝐵𝑆)]

8𝑛 − 3𝑎𝑆2 (𝑁2

𝐵+ 𝑁2

𝐴)

.

(8)

Therefore, 𝑓∗𝐴BC = 𝑓

∗

𝐵BC when 𝑁𝐴= 𝑁𝐵. Proposition 10


(3) The Third Form: The Form of Cooperation. The full trustworking relationship between enterprises has been com-pletely established under the situation of cooperation. Thusthe food price and the quality effort efficiency can be deter-mined by both enterprises 𝐴 and 𝐵.

Proposition 11. There exists local maximum in the overallprofits of the food supply chain under the situation of cooper-ation, and the downstream enterprise’s quality effort efficiencyis equal to the upstream enterprise when𝑁

𝐴= 𝑁𝐵.

Demonstration. The sale price of food is determined by bothenterprises 𝐴 and 𝐵 in the second stage and the profitfunction of the whole food supply chain is as follows;

𝐿HC = {𝑝 − [𝑐𝐴 + 𝑐𝐵 + 𝑁𝐴𝑆 (1 − 𝑓𝐴) + 𝑁𝐵𝑆 (1 − 𝑓𝐵)]}

⋅ (𝑁 − 𝑎𝑝) −1

2𝑛 (𝑓2

𝐴+ 𝑓2

𝐵) .

(9)

Let 𝜕𝐿HC/𝜕𝑝 = 0, and 𝑝∗HC, 𝑄∗

HC can be obtained, asfollows:

𝑝∗

HC

=𝑁 + 𝑎 [𝑐


𝐴) + 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]

2𝑎

𝑄∗

HC

=𝑁 − 𝑎 [𝑐


𝐴) + 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]

2.

(10)

Bring 𝑝∗HC and 𝑄∗HC into (9), and Hessian Matrix can beobtained, as follows:

𝐻HC = (

𝜕2𝐿HC𝜕𝑓2

𝐴

𝜕2𝐿HC

𝜕𝑓𝐴𝜕𝑓𝐵

𝜕2𝐿BC

𝜕𝑓𝐵𝜕𝑓𝐴

𝜕2Ω

𝜕𝑓2

𝐵

)

=(

𝑎𝑁2

𝐴𝑆2

2− 𝑛

𝑎𝑁𝐴𝑁𝐵𝑆2

2

𝑎𝑁𝐴𝑁𝐵𝑆2

2

𝑎𝑁2

𝐵𝑆2

2− 𝑛

) .

(11)

Therefore, there exists local maximum in the overall prof-its of the food supply chain due to |𝐻HC| = 𝑛[𝑛 − (𝑎𝑆

2(𝑁2

𝐴+

𝑁2

𝐵))/2] > 0. Let 𝜕𝐿HC/𝜕𝑓𝐴 = 0, 𝜕𝐿HC/𝜕𝑓𝐵 = 0; thus


the optimal values of quality efforts efficiency of both enter-prises 𝐴 and 𝐵 under the situation of cooperation can beobtained through solving the simultaneous equations, asfollows:

𝑓∗

𝐴HC =𝑁𝐴𝑆 [𝑁 − 𝑎 (𝑐


𝐵𝑆)]

2𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 𝑁2

𝐴)

,

𝑓∗

𝐵HC =𝑁𝐵𝑆 [𝑁 − 𝑎 (𝑐


𝐵𝑆)]

2𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 𝑁2

𝐴)

.

(12)

Therefore 𝑓∗𝐴HC = 𝑓

∗

𝐵HC when 𝑁𝐴= 𝑁𝐵. Proposition 11


2.2. TheTheoretical Analysis of Contact Mechanism Design

2.2.1. Interaction Effects between the Upstream andDownstream Enterprises

Proposition 12. The extent of quality efforts for food safetymust be greater than a certain value, namely, 𝛿, and then thequality efforts can be productive.

Demonstration. With (4), the following equations can beobtained due to 0 ≤ 𝑓

𝑖= Δ𝑁

𝑖/𝑁𝑖(𝑖 = 𝐴, 𝐵) < 1:

4𝑛 > 𝑁𝐴𝑆 {𝑁 − 𝑎 [𝑐

𝐴+ 𝑐𝐵+ 𝑁𝐵𝑆 (1 − 𝑓

𝐵)]} ,

8𝑛 > 𝑁𝐵𝑆 {𝑁 − 𝑎 [𝑐


𝐴)]} .

(13)

The equation𝑁 − 𝑎[𝑐𝐴+ 𝑐𝐵+ 𝑁𝐵𝑆(1 − 𝑓

𝐵)] or𝑁 − 𝑎[𝑐

𝐴+

𝑐𝐵+ 𝑁𝐴𝑆(1 − 𝑓

𝐴)] can be represented as a kind of food

demands, which is when the upstream or downstream enter-prise makes quality efforts and downstream or upstreamenterprise is not profitable.The equation𝑁

𝐴𝑆{𝑁−𝑎[𝑐

𝐴+𝑐𝐵+


𝐵)]} or𝑁

𝐵𝑆{𝑁 − 𝑎[𝑐

𝐴+ 𝑐𝐵+ 𝑁𝐴𝑆(1 − 𝑓

𝐴)]} can be

represented as a loss that these demands caused in the foodsafety incidents. Only when the extent of quality efforts isgreater than the loss that the food safety incidents caused canthe quality efforts efficiency be achieved. Therefore, qualityefforts of enterprises can achieve some kind of effectivenessonlywhen 𝑛 > (1/4)𝑁


𝐴+𝑐𝐵+𝑁𝐵𝑆(1−𝑓

𝐵)]}; namely,

𝛿 = (1/4)𝑁𝐴𝑆{𝑁 − 𝑎[𝑐

𝐴+ 𝑐𝐵+ 𝑁𝐵𝑆(1 − 𝑓

𝐵)]}. Proposition 12


Proposition 13. If one wants to reduce the probability offood safety incidents when the average number of quality andsafety events of per unit food of the upstream and downstreamenterprises in one year is the same, one should pay attentionto strengthening regulation over the source of the food supplychain. The same number of quality efforts investments canachieve more quality efforts effectiveness in the upstreamenterprise.

Demonstration. We can find that the equation 𝑓𝐴≥ 𝑓𝐵can

always be obtained when 𝑁𝐴= 𝑁𝐵through comparing

the quality efforts efficiency of enterprises 𝐴 and 𝐵 underthe three different forms of cooperation. Therefore, Propo-sition 13 has been demonstrated to be correct.

Proposition 14. The quality efforts behavior of the upstreamor downstream enterprises can encourage the downstream orupstream enterprises to carry out quality efforts.

Demonstration. It can be seen from the inequality 4𝑛 >

𝑁𝐴𝑆{𝑁 − 𝑎[𝑐

𝐴+ 𝑐𝐵+ 𝑁𝐵𝑆(1 − 𝑓

𝐵)]} that the improvement of

the quality efforts efficiency of enterprise 𝐵 will increase thedifficulty of enterprise 𝐴 obtaining the same quality effortsefficiency. Therefore, enterprise 𝐴 is bound to increase theamount of quality efforts investment if it wants to achievethe original quality efforts efficiency due to the reason thatthe enterprise 𝐴 shares part of the quality effort costs forenterprise𝐵. It can be seen from the inequality 4𝑛 > 𝑁

𝐴𝑆{𝑁−

𝑎[𝑐𝐴+ 𝑐𝐵]} that the quality efforts efficiency of enterprise 𝐴

will be improved obviously when lim𝑓𝐵,𝑆→0


𝐵) = 0.

Thus, Proposition 14 has been demonstrated to be correct.

Proposition 15. The extent of quality efforts is directly pro-portional to the average number of quality and safety eventsof per unit food of an enterprise in one year and is inverselyproportional to the average number of quality and safety eventsof per unit food of another enterprise in one year. Namely,for food companies, the more the average number of qualityand safety events of the unit food in one year, the greater theresistance of that enterprise to carry out quality efforts.

Demonstration. Assume that the extents of quality efforts ofthe two main participant bodies are the same. It can be seenfrom the inequality 4𝑛 > 𝑁


𝐴+𝑐𝐵+𝑁𝐵𝑆(1−𝑓

𝐵)]} that

𝑛 is directly proportional to𝑁𝐴and is inversely proportional

to 𝑁𝐵. In the same way, it can be seen from the inequality

8𝑛 > 𝑁𝐵𝑆{𝑁 − 𝑎[𝑐

𝐴+ 𝑐𝐵+ 𝑁𝐴𝑆(1 − 𝑓

𝐴)]} that 𝑛 is inversely

proportional to 𝑁𝐴and is directly proportional to 𝑁

𝐵. If

the difficulty coefficients of quality efforts of the two mainparticipant bodies are not the same, then there exists 𝑛

𝐴and

𝑛𝐵simultaneously; 𝑛

𝐴is directly proportional to 𝑁

𝐴and is

inversely proportional to 𝑁𝐵; 𝑛𝐵is inversely proportional to

𝑁𝐴and is directly proportional to 𝑁

𝐵. Therefore, Proposi-

tion 15 has been demonstrated to be correct.

2.2.2. The Comparison of the Average Number of Quality andSafety Events of per Unit Food of theWhole Food Supply Chainin One Year and the Enterprises’ Quality Efforts Efficiencyunder Different Forms of Cooperation. After the enterprises𝐴 and 𝐵 carried out quality efforts, the average number ofquality and safety events of per unit food of the whole foodsupply chain in one year under different forms of cooperation,respectively, is as follows:

𝑁∗

NC = 𝑁𝐴 (1 − 𝑓∗

𝐴NC) + 𝑁𝐵 (1 − 𝑓∗

𝐵NC)

=

8𝑛 (𝑁𝐴+ 𝑁𝐵) − 𝑆 (𝑁

2

𝐵+ 2𝑁2

𝐴) [𝑁 − 𝑎 (𝑐

𝐴+ 𝑐𝐵)]

8𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 2𝑁2

𝐴)

𝑁∗

BC = 𝑁𝐴 (1 − 𝑓∗

𝐴BC) + 𝑁𝐵 (1 − 𝑓∗

𝐵BC)

=

8𝑛 (𝑁𝐴+ 𝑁𝐵) − 3𝑆 (𝑁

2

𝐵+ 𝑁2

𝐴) [𝑁 − 𝑎 (𝑐

𝐴+ 𝑐𝐵)]

8𝑛 − 3𝑎𝑆2 (𝑁2

𝐵+ 𝑁2

𝐴)


𝑁∗

HC = 𝑁𝐴 (1 − 𝑓∗

𝐴HC) + 𝑁𝐵 (1 − 𝑓∗

𝐵HC)

=

2𝑛 (𝑁𝐴+ 𝑁𝐵) − 𝑆 (𝑁

2

𝐵+ 𝑁2

𝐴) [𝑁 − 𝑎 (𝑐

𝐴+ 𝑐𝐵)]

2𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 𝑁2

𝐴)

.

(14)Proposition 16. The average number of quality and safetyevents of per unit food of the whole food supply chain in oneyear will decrease with the increase of the extent of cooperation.

Demonstration. It can be seen from the inequality 𝑁∗NC −𝑁∗

BC > 0 and 𝑁∗BC − 𝑁∗

HC > 0 that 𝑁∗NC > 𝑁∗

BC > 𝑁∗

HC.Therefore, Proposition 16 has been demonstrated to be cor-rect.

Proposition 17. The quality efforts efficiency of enterprisesin the state of cooperation is higher than that in the stateof noncooperation. Therefore, only with strengthening thequality efforts cooperation between upstream and downstreamenterprises can the higher effectiveness on guaranteeing foodsafety be achieved in the process of strengthening the food safetyguarantee.

Demonstration. It can be seen from the inequality 𝑓∗𝐴BC −

𝑓∗

𝐴NC > 0 and 𝑓∗𝐴HC − 𝑓

∗

𝐴BC > 0 that 𝑓∗𝐴HC > 𝑓

∗

𝐴BC >

𝑓∗

𝐴NC. And the inequality 𝑓∗𝐵HC > 𝑓

∗

𝐵BC > 𝑓∗

𝐵NC can beobtained in the same way. Therefore, Proposition 17 has beendemonstrated to be correct.

2.2.3. The Influence of the Loss 𝑆That Food Quality and SafetyIncidents Caused on the Quality Efforts Efficiency. Assumethat 𝑁

𝐴= 𝑁𝐵= 1, 𝑐

𝐴= 𝑐𝐵= 0, and 𝑎 = 1 in order to

simplify the calculation; thus 𝑓∗𝐴NC = 2𝑆(𝑁 − 2𝑆)/(8𝑛 − 3𝑆

2),

𝑓∗

𝐵NC = 𝑆(𝑁 − 2𝑆)/(8𝑛 − 3𝑆2), 𝑓∗NC = 3𝑆(𝑁 − 2𝑆)/(8𝑛 − 3𝑆

2),

𝑓∗

𝐴BC = 3𝑆(𝑁−2𝑆)/(8𝑛− 6𝑆2), 𝑓∗𝐵BC = 3𝑆(𝑁−2𝑆)/(8𝑛− 6𝑆

2),

𝑓∗

BC = 6𝑆(𝑁 − 2𝑆)/(8𝑛 − 6𝑆2), 𝑓∗𝐴HC = 𝑆(𝑁 − 2𝑆)/(2𝑛 − 2𝑆

2),

𝑓∗

𝐵HC = 𝑆(𝑁 − 2𝑆)/(2𝑛 − 2𝑆2), and 𝑓∗HC = 𝑆(𝑁 − 2𝑆)/(𝑛 − 𝑆

2).

It can be seen from the above formula that the quality effortsefficiency is affected by the 𝑆 fluctuations.

Proposition 18. The quality efforts efficiency of the wholesupply chain is the highest under the situation that enterprise𝐴 cooperates with enterprise 𝐵 and is the lowest under thenoncooperation situation.

Demonstration. It can be seen from the inequality 𝑓∗HC >

𝑓∗

BC > 𝑓∗

NC that Proposition 18 is obviously correct.

Proposition 19. The quality efforts efficiency is directly pro-portional to the loss S that the average quality and safetyevents of per unit food caused each time under the differentcooperation modalities. If the enterprise 𝐴 is uncooperativewith the enterprise 𝐵, then the larger value of the qualityefforts efficiency can be obtained, and the increments of thequality efforts efficiency gradually increase when S is relativelylarge. If the enterprise 𝐴 is cooperative with the enterprise 𝐵,then the larger value of the quality efforts efficiency can be

obtained, but the increments of the efficiency of quality effortsgradually decreasewhen 𝑆 is relatively small. And the sensitivitycoefficient of the quality efforts efficiency of the food supplychain to 𝑆 is the highest in the case of cooperation and is thelowest in the case of noncooperation.

Demonstration. Take the noncooperation situation for exam-ple. It can be seen from the equation 𝜕𝑓∗NC/𝜕𝑆 = (9𝑁𝑆

2−

96𝑛𝑆+24𝑛𝑁)/(8𝑛−3𝑆2)2 that𝑓∗NC is directly proportional to 𝑆

when 9𝑁𝑆2−96𝑛𝑆+24𝑛𝑁 > 0. Let𝑓(𝑆) = 9𝑁𝑆2−96𝑛𝑆+24𝑛𝑁;thus Δ = 32𝑛 − 3𝑆2 when 𝑓(𝑆) = 0.

(1) There are no intersection points between the curve𝜕𝑓∗

NC/𝜕𝑆 and the 𝑆 axis (as curve Ι which is shownin Figure 2) when Δ < 0; namely, the inequality𝜕𝑓∗

NC/𝜕𝑆 > 0 is always stand-up, and 𝑓∗NC is directlyproportional to 𝑆. Curve ΙΙ can be derived from curveΙ. It can be seen from curve ΙΙ that Δ𝑓∗NC is decreasingwith the increase of 𝑆 when 𝑆 is relatively small, andΔ𝑓∗

NC is increasing with the increase of 𝑆 due to thereason that enterprises increase the quality effortsinvestment when 𝑆 is relatively large which resultsin the increasing of the probability of bankruptcycrisis to be faced by food companies (e.g., Sanlu MilkPowder Incident in 2008).

(2) The curve 𝜕𝑓∗NC/𝜕𝑆 intersects the 𝑆 axis at two pointswhen Δ > 0, namely, 𝑆− and 𝑆+ (as curve ΙΙ which isshown in Figure 2). When 𝑆 ∈ (0, 𝑆−),the inequality𝜕𝑓∗

NC/𝜕𝑆 > 0, 𝜕2𝑓∗

NC/𝜕𝑆2< 0 can be obtained; thus

𝑓∗

NC is directly proportional to 𝑆; Δ𝑓∗NC is decreasingwith the increase of 𝑆. When 𝑆 = 𝑆

−, the equation𝜕𝑓∗

NC/𝜕𝑆 = 0 can be obtained, and the quality effortsefficiency achieves the maximum 𝑓NC(max) at themoment. When 𝑆 ∈ (𝑆

−, 𝑆+), the inequality 𝜕𝑓∗NC/

𝜕𝑆 < 0 can be obtained, but the quality efforts effi-ciency decreases at a faster pace due to the reasonthat the food companies have the speculative men-tality during the inception phase, which relies on theinsurance companies’ compensation or the govern-ment’s subsidies instead of carrying out quality effortsto fill up the loss. When it reduces to the lowestpoint, namely, the turning point 𝐸, they will considerincreasing the quality efforts investment under theinfluence of the dual pressures which are from thedecreasing of the quality efforts efficiency and theincreasing of the probability of bankruptcy crisis to befaced by food companies.Thequality efforts efficiencywill not stop decreasing for increasing the qualityefforts investment, but the amplitude of the decreasewill be smaller and smaller due to the inertia action.When 𝑆 = 𝑆

+, the equation 𝜕𝑓∗NC/𝜕𝑆 = 0 can beobtained, and the quality efforts efficiency achievesthe minimum 𝑓NC(min) at the moment. When 𝑆 ∈

(𝑆+, +∞), the inequality 𝜕𝑓∗NC/𝜕𝑆 > 0, 𝜕

2𝑓∗

NC/𝜕𝑆2> 0

can be obtained; thus 𝑓∗NC is directly proportional to𝑆; Δ𝑓∗NC is increasing with the increase of 𝑆.


𝜕f∗NC𝜕S

III

S−S

S+0

(a)

S−S

S+

f∗NC

fNC (max)

fNC (min)

Turning point E

III

IV

0

(b)

Figure 2: Relations between 𝜕𝑓∗NC/𝜕𝑆, 𝑓∗NC, and 𝑆.

HΔ > 0

HΔ < 0

0

BΔ < 0 BΔ > 0

NΔ < 0

NΔ > 0

S

𝜕f∗NC𝜕S

(a)

HΔ > 0

HΔ < 0BΔ < 0

BΔ > 0NΔ > 0

NΔ < 0

0 S

f∗NC

(b)

Figure 3: Relations between 𝜕𝑓∗NC/𝜕𝑆, 𝑓∗NC, and 𝑆 in the conditions of three kinds of cooperation modalities.

The proving process which is under the situation of non-cooperation is the same as that under the situation of sem-icooperation and cooperation. Only the curve gradient andthe intersection point range of the abscissa are differentunder the three kinds of cooperation modalities, as shownin Figure 3. It can be seen from Figure 3 that 𝑆 which themaximum value of the quality efforts efficiency correspondsto when the enterprise 𝐴 is cooperative with enterprise 𝐵 isless than that under the situation of noncooperation; namely,cooperative enterprises are more inclined to accommodatethe smaller 𝑆. Therefore, the larger value of the quality effortsefficiency can be obtained if the enterprises 𝐴 and 𝐵 arecooperative when 𝑆 is relatively small; conversely, the largervalue of the quality efforts efficiency can also be obtained ifthe enterprises are uncooperative when S is relatively large.Meanwhile, Figure 3(b) shows that the great fluctuation inthe quality efforts efficiency of the food supply chain will becaused by the small Δ𝑆 under the situation of cooperation.And even if the large Δ𝑆 cannot give rise to the great

fluctuation in the quality efforts efficiency under the situationof noncooperation, the sensitivity coefficient of the qualityefforts efficiency to 𝑆 is the highest in the case of cooperationand is the lowest in the case of noncooperation. Therefore,Proposition 19 has been demonstrated to be correct.

2.2.4. The Profits of the Food Supply Chain under the Dif-ferent Cooperation Situations. Plug the above calculationalresults into the profit functions, and the profit functions ofenterprises under the different cooperation situations can beobtained, as follows.

Noncooperation:

𝐿∗

𝐴NC = (8𝑛2

𝑎− 2𝑛𝑁

2

𝐴𝑆2)

⋅[𝑁 − 𝑎 (𝑐


𝐵𝑆)]2

[8𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 2𝑁2

𝐴)]2

,


𝐿∗

𝐵NC = (4𝑛2

𝑎−1

2𝑛𝑁2

𝐵𝑆2)

⋅[𝑁 − 𝑎 (𝑐


𝐵𝑆)]2

[8𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 2𝑁2

𝐴)]2

,

𝐿∗

NC = [12𝑛2

𝑎−1

2𝑛𝑆2(4𝑁2

𝐴+ 𝑁2

𝐵)]

⋅[𝑁 − 𝑎 (𝑐


𝐵𝑆)]2

[8𝑛 − 𝑎𝑆2 (𝑁2

𝐵+ 2𝑁2

𝐴)]2

.

(15)

Semicooperation:

𝐿∗

𝐴BC = (8𝑛2

𝑎−9

2𝑛𝑁2

𝐴𝑆2)

⋅[𝑁 − 𝑎 (𝑐


𝐵𝑆)]2

[8𝑛 − 3𝑎𝑆2 (𝑁2

𝐵+ 𝑁2

𝐴)]2

,

𝐿∗

𝐵BC = (4𝑛2

𝑎−9

2𝑛𝑁2

𝐵𝑆2)

⋅[𝑁 − 𝑎 (𝑐


𝐵𝑆)]2

[8𝑛 − 3𝑎𝑆2 (𝑁2

𝐵+ 𝑁2

𝐴)]2

,

𝐿∗

BC = [12𝑛2

𝑎−9

2𝑛𝑆2(𝑁2

𝐴+ 𝑁2

𝐵)]

⋅[𝑁 − 𝑎 (𝑐


𝐵𝑆)]2

[8𝑛 − 3𝑎𝑆2 (𝑁2

𝐴+ 𝑁2

𝐵)]2

.

(16)

Cooperation:

𝐿∗

HC = [𝑛2

𝑎−1

2𝑛𝑆2(𝑁2

𝐴+ 𝑁2

𝐵)]

⋅[𝑁 − 𝑎 (𝑐


𝐵𝑆)]2

[2𝑛 − 𝑎𝑆2 (𝑁2

𝐴+ 𝑁2

𝐵)]2

.

(17)

Proposition 20. The higher the extent of cooperation in thequality and safety between the upstream and downstreamenterprises, the higher the profits of the whole food supplychain that can be achieved. Therefore, one should strengthencooperation between the upstream and downstream enterprisesin the process of carrying out quality efforts.

Demonstration. It can be seen from the inequality 𝐿∗𝐵BC > 0

that 4𝑛2/𝑎 − (9/2)𝑛𝑁2𝐵𝑆2> 0 under the situation of semi-

cooperation. Meanwhile the inequality 4𝑛−3𝑎𝑆2(𝑁2𝐴+𝑁2

𝐵) >

0 and 𝑛 − 𝑎𝑆2(𝑁2𝐴+ 𝑁2

𝐵) > 0 can be obtained through

comparing the profit function values under the differentcooperation situations. Therefore, the inequality 𝐿∗BC > 𝐿

∗

NCand 𝐿∗HC > 𝐿

∗

BC can be obtained; namely, 𝐿∗HC > 𝐿∗

BC > 𝐿∗

NC.Proposition 20 has been demonstrated to be correct.

2.2.5. The Social Welfare Comparison without Considering theExternality under Different Cooperation Situations. Regard-less of the externality, (the sum of the producer surplus andconsumer surplus is social welfare regardless of the external-ity) the social welfare is that

𝑊 = ∫

𝑄∗

0

(𝑁 − 𝑥

𝑎− 𝑐𝑖)𝑑𝑥 −

1

2𝑛𝑓2

= (𝑁

𝑎− 𝑐𝑖)𝑄∗−𝑄∗2

2𝑎−1

2𝑛𝑓2.

(18)

Bring the simplified demand functions into (18), and thenthe simplified social welfare expressions under the differentcooperation situations can be obtained, as follows:

𝑊∗

NC

=2𝑛 (𝑁 − 2𝑆)

8𝑛 − 3𝑆2[𝑁 −

𝑛 (𝑁 − 2𝑆)

8𝑛 − 3𝑆2−9

4

𝑆2(𝑁 − 2𝑆)

8𝑛 − 3𝑆2] ,

𝑊∗

BC

=2𝑛 (𝑁 − 2𝑆)

8𝑛 − 6𝑆2[𝑁 −

𝑛 (𝑁 − 2𝑆)

8𝑛 − 6𝑆2−9𝑆2(𝑁 − 2𝑆)

8𝑛 − 6𝑆2] ,

𝑊∗

HC

=𝑛 (𝑁 − 2𝑆)

2𝑛 − 2𝑆2[𝑁 −

1

2

𝑛 (𝑁 − 2𝑆)

2𝑛 − 2𝑆2−2𝑆2(𝑁 − 2𝑆)

2𝑛 − 2𝑆2] .

(19)

Proposition 21. Social welfare will increase with the increaseof the extent of cooperation on the quality and safety betweenthe upstream and downstream enterprises without consideringthe externality influence caused by food safety incidents.

Demonstration. Due to 𝑊∗BC − 𝑊∗NC > 0, 4((9/2)𝑆3 − (21/4)𝑁𝑆2) < 18𝑆

3−15𝑁𝑆

2, 8𝑛−6𝑆2 < 8𝑛−3𝑆2; thus the inequality𝑊∗

HC − 𝑊∗

BC > 0 can be obtained; namely, 𝑊∗HC > 𝑊∗

BC >

𝑊∗

NC. Therefore, Proposition 21 has been demonstrated to becorrect.

3. The Analysis of the Factors WhichInfluence the Enterprises’ CollaborationStrategy for the Quality and Safety

Theclose cooperation between all of the links (the node enter-prises) in the food supply chain can be realized throughestablishing the cooperation, incentive, and supervisionmechanism. However, the macro environment (includingthe related governmental policies and laws that continue tomove forward in a timely fashion and the general public (theconsumers’ consumption habit, the consumption concept,consumption evaluation, consumption quality migration,news media exposure, etc.)) and the micro environment(company’s earnings in future, etc.) will also be the importantbasis for companies’ decision-making in the process of coop-eration between the upstream and downstream enterprises.


Table 1: The strategic payoff matrix of the game.

Enterprise 𝐴 Enterprise 𝐵𝐵1(𝑞) 𝐵

2(1 − 𝑞)

𝐴1(𝑝)

𝑞𝐶(𝑐1− 𝑘1) + 𝑔 + V

𝑞𝐶(𝑐2− 𝑘2) + 𝑔 + V

𝑞𝐶(𝑐1− 𝑘1) + 𝑔 + V

𝑙2−𝑠−𝛿[𝜂𝜙ℎ+𝜂(1−𝜙)𝜑𝑚+(1−𝜂)𝑚]−Δ𝑘

𝐴2(1 − 𝑝) 𝑙

1− 𝑠 − 𝛿[𝜂𝜙ℎ + 𝜂(1 − 𝜙)𝜑𝑚 + (1 − 𝜂)𝑚] − Δ𝑘, 𝑞

𝐶(𝑐2− 𝑘2) + 𝑔 + V −𝛿[𝜂𝜙ℎ + 𝜂(1 − 𝜙)𝜑𝑚 + (1 − 𝜂)𝑚] − Δ𝑘

−𝛿[𝜂𝜙ℎ + 𝜂(1 − 𝜙)𝜑𝑚 + (1 − 𝜂)𝑚] − Δ𝑘

Note. p, q are the proportion of the individuals in two game groups who choose the strategies 𝐴1 and 𝐴2.

The above model hypothesis does not take into account themacro environment and the micro environment variables.

Therefore, analyzing the enterprises’ behavioral charac-teristics in the process of cooperation and the factors whichinfluence enterprises’ collaboration strategy for the qualityefforts is new expansion of researches on the enterprises’ col-laboration strategy for the quality and safety in the con-ventional sense through applying evolutionary economicsapproach and introducing themacro andmicro environmentvariables to construct evolutionary game model.

3.1. The Establishment of the Model

Assumption 1. The benefits that the unit quality efforts canbring for the enterprises 𝐴 and 𝐵, respectively, are 𝑐

1, 𝑐2. The

cost of per unit quality efforts that enterprises𝐴 and𝐵 shouldpay for, respectively, is 𝑘

1, 𝑘2. The output of both enterprises

is 𝑞𝐶. The earnings of enterprise 𝐴 that does not carry out

quality efforts are 𝑙1when the enterprise 𝐵 carries out quality

efforts; the market demand will increase due to the qualityefforts of enterprise 𝐵 at the moment, and the benefits ofhitchhiking of the enterprise 𝐴 can be realized when it doesnot increase input.The earnings of enterprise 𝐵 that does notcarry out quality efforts are 𝑙

2when the enterprise 𝐴 carries

out quality efforts; themarket demandwill increase due to thequality efforts of enterprise𝐴 at themoment, and the benefitsof hitchhiking of the enterprise𝐵 can be realized when it doesnot increase input.

Assumption 2. Thegovernmentwill grant subsidies which are𝑔 to the enterprises that carry out quality efforts. The super-visory departments will strictly monitor and punish theenterprises that do not carry out quality efforts in orderto hurt their chances of hitchhiking, and the penalty is 𝑚;the supervision efficiency is 𝛿. Consumers expose the enter-prises’ hitchhiking behavior through their own evaluationmechanism; the enterprises’ beneficial losses (e.g., reputation,integrity) caused by it are 𝑠 (𝑠 < min(𝑙

1, 𝑙2)). But there

may exist the power rent-seeking behavior in the supervisoryprocess; the probability of it is 𝜂; therefore, the enterprisesthat do not carry out quality efforts can avoid the penaltythrough offering bribes (the probability is 𝜙; the bribesare ℎ) to the supervisory departments. The penalty for thesupervisory departments which will abuse their authoritycharge illegally is 𝜑𝑚 (𝜑 > 1) if they do not bribe them(the probability is 1 − 𝜙). Meanwhile, consumers have strongcognitive ability about food quality and safety; they are ableto identify different quality of products and are willing to pay

the price discrimination and their demands will increasebecause of the enterprises’ quality efforts strategy; then thebenefits that can be brought are V. The general public’s super-vision, including news media and consumers, and the actionto expose the supervisory departments’ laziness behavior, thecollusion behavior between local governments and firms, thepower rent-seeking behavior, and so forth can increase thedefensive costs of the potential enterprises that do not carryout quality efforts, which are Δ𝑘.

This paper constructs the strategic payoff matrix of thegame between enterprise 𝐴 group and enterprise 𝐵 groupbased on the above assumptions, as shown in Table 1.

If the adaptability of adopting a strategy is higher thanthe average adaptability of the group, then the probabilityof adopting the strategy will increase gradually as time 𝑡goes on [32] according to theMalthusian dynamic equations.The replication dynamic differential equations of the strategyinteraction between enterprises 𝐴 and 𝐵 evolving with timecan be obtained based on the methods that the literatures[33, 34] proposed, as follows:

𝑑𝑝

𝑑𝑡= 𝑝 (1 − 𝑝) {𝑞 (𝑠 − 𝑙

1) + 𝑞𝐶(𝑐1− 𝑘1) + 𝑔 + V

+ 𝛿 [𝜂𝜙ℎ + 𝜂 (1 − 𝜙) 𝜑𝑚 + (1 − 𝜂)𝑚] + Δ𝑘} ,

𝑑𝑞

𝑑𝑡= 𝑞 (1 − 𝑞) {𝑝 (𝑠 − 𝑙

2) + 𝑞𝐶(𝑐2− 𝑘2) + 𝑔 + V

+ 𝛿 [𝜂𝜙ℎ + 𝜂 (1 − 𝜙) 𝜑𝑚 + (1 − 𝜂)𝑚] + Δ𝑘} .

(20)

Let 𝑑𝑝/𝑑𝑡 = 0, 𝑑𝑞/𝑑𝑡 = 0; we can draw the evolutionaryphase diagram of the game (Figure 9(a)) and work out theequilibrium points of the system equations that are (0, 0),(0, 1), (1, 0), (1, 1), (𝑝∗, 𝑞∗)when 𝜂 < min{(𝑙

2−𝑠−𝑞𝐶(𝑐2−𝑘2)−

𝑔−V−Δ𝑘−𝛿𝑚)/𝛿[𝜙ℎ+(1−𝜙)𝜑𝑚−𝑚], (𝑙1−𝑠−𝑞

𝐶(𝑐1−𝑘1)−𝑔−

V − Δ𝑘 − 𝛿𝑚)/𝛿[𝜙ℎ + (1 − 𝜙)𝜑𝑚 −𝑚]}.𝑁 (0, 1), 𝑊 (1, 0) areinstability points, 𝐺 (𝑝∗, 𝑞∗) is the saddle point, and 𝑂(0, 0),𝑀(1, 1) are evolutionary stable strategy (ESS) according tothe matrix Jacobian characteristic value theorem. It can beseen from Figure 9(a) that regime I is the probability of thesystem converging to the locked equilibrium status model(𝐴2, 𝐵2) and regime II is the probability of the system

converging to the ideal equilibrium status model (𝐴1, 𝐵1).

3.2. The Analysis of the Macro Factors Which Influence theCooperation Strategy. Considering the complexity of thecomputation on the game equilibrium results, this paper ana-lyzes themechanism that the change ofmacro-environmental


0 10 20 30 40 50 60−0.2

0

0.2

0.4

0.6

0.8

1

1.2

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(a) 𝑔 = 1

0 10 20 30 40 50 600.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(b) 𝑔 = 3

Figure 4: The influence of the government’s positive stimulus on the cooperation strategy.

0 10 20 30 40 50 60−0.2

0

0.2

0.4

0.6

0.8

1

1.2

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(a) 𝛿 = 0.1

0 10 20 30 40 50 600.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(b) 𝛿 = 0.8

Figure 5: The influence of the government’s supervision efficiency on the cooperation strategy.

variables influences the evolution of the cooperation strategybehavior with the help of Matlab to conduct the numericalexample simulations. With reference to the related literatures[35–37], the following parameters are set to 𝑐

1= 3, 𝑐

2= 2,

𝑘1= 2, 𝑘

2= 1, 𝑞

𝐶= 2, 𝑙1= 9.5, 𝑙

2= 9, 𝑔 = 1,𝑚 = 2, 𝛿 = 0.1,

𝑠 = 0.5, 𝜂 = 0.5, 𝜙 = 0.2, ℎ = 1.5, 𝜑 = 1.5, V = 1, and Δ𝑘 = 1.The results of numerical simulation experiments are shownin Figures 4–8.

It can be seen from the numerical simulation results thatthe government’s positive stimulus, efficient regulation, and

appropriate punishment, the consumers’ positive guidance,and the news media’s efficient disclosure mechanism canencourage the enterprises to increase investment in qualityefforts and strengthen the enterprises’ cooperation strategyfor the quality efforts.

Through comparing Figure 6(a) with Figures 6(b) and6(c), we can find an interesting phenomenon that the proba-bility of the rail line converging to the ideal equilibrium statusincreases significantly and even can be completely evolvedto the ideal equilibrium status model with the increase of


0 10 20 30 40 50 60−0.2

0

0.2

0.4

0.6

0.8

1

1.2

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(a) 𝑚 = 2

0 10 20 30 40 50 600.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(b) 𝑚 = 4

0 10 20 30 40 50 60−0.2

0

0.2

0.4

0.6

0.8

1

1.2

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(c) 𝑚 = 10

Figure 6: The influence of the punishing dynamics of government on the cooperation strategy.

the punishing dynamics, but it will increase the uncertaintyof the evolutionary path when the punishing dynamics arebeyond the limits. It can be seen from Figure 6(c) that therail line at 𝑝0 = 0.5 boundaries converges to two modesand the probability of the rail line converging to the lockedequilibrium statusmodel is higher. It seems that this is in con-tradiction with what we have done in reality that we shouldincrease the punishing dynamics for the quality inexertionactions if we want to boost enterprises’ cooperation incentive.The explanation and the demonstration for this point can bedescribed as the follows:

𝑙2− 𝑠 − 𝛿𝜂𝜙ℎ − 𝛿𝜂 (1 − 𝜙) 𝜑𝑚 − 𝛿 (1 − 𝜂)𝑚 − Δ𝑘

− 𝑞𝐶(𝑐2− 𝑘2) − 𝑔 − V > 0.

(21)

Take the derivative of the inequality’s left sidewith respectto𝑚, and the following inequality can be obtained, as follows:

−𝛿𝜂 (1 − 𝜙) 𝜑 − 𝛿 (1 − 𝜂) < 0. (22)

It indicates that the income difference that companiesadhere to carry out quality efforts changes in the oppositedirection with the change of 𝑚. Therefore, appropriate pun-ishment will be conducive to jumping out of the locked status,and excessive punishment can easily lead to the governmentdepartments slacking offmore and choosing the strategy thatdoes not supervise enterprises.

3.3. The Analysis of the Micro Factors Which Influence theCooperation Strategy. Suppose the opportunity income’s lossthat is caused due to the reason that the enterprises 𝐴 and 𝐵


0 10 20 30 40 50 60−0.2

0

0.2

0.4

0.6

0.8

1

1.2

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(a) 𝑠 = 0.5/V = 1

0 10 20 30 40 50 600.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(b) 𝑠 = 3/V = 3

Figure 7: The influence of the consumers’ positive guidance on the cooperation strategy.

0 10 20 30 40 50 60−0.2

0

0.2

0.4

0.6

0.8

1

1.2

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(a) Δ𝑘 = 1

0 10 20 30 40 50 60−0.2

0

0.2

0.4

0.6

0.8

1

1.2

p0 = 0.9

p0 = 0.6

p0 = 0.4

p0 = 0.1

q

t

(b) Δ𝑘 = 4

Figure 8: The influence of the news media’s disclosure mechanism on the cooperation strategy.

do not choose the cooperation strategy is 𝑙𝐴, 𝑙𝐵. The discount

factor of the enterprise future earnings (it can reflect thedegree of mutual trust between the enterprises and enter-prises concern about the extra income they can receive fromthe future cooperation) is 𝜀

𝐴, 𝜀𝐵. Meanwhile, the replication

dynamic differential equations of the strategy interactionbetween enterprises 𝐴 and 𝐵 evolving with time can beobtained by introducing the future earnings factor into theabove model, as follows:

𝑑𝑝

𝑑𝑡= 𝑝 (1 − 𝑝) {𝑞 (𝑠 − 𝑙

1) + 𝑞𝐶(𝑐1− 𝑘1) + 𝑔 + V

+ 𝛿 [𝜂𝜙ℎ + 𝜂 (1 − 𝜙) 𝜑𝑚 + (1 − 𝜂)𝑚] + Δ𝑘

+ 𝑙𝐴𝜀𝐴} ,

𝑑𝑞

𝑑𝑡= 𝑞 (1 − 𝑞) {𝑝 (𝑠 − 𝑙

2) + 𝑞𝐶(𝑐2− 𝑘2) + 𝑔 + V

+ 𝛿 [𝜂𝜙ℎ + 𝜂 (1 − 𝜙) 𝜑𝑚 + (1 − 𝜂)𝑚] + Δ𝑘

+ 𝑙𝐵𝜀𝐵} .

(23)

We can draw the evolutionary phase diagram of the game(Figure 9(b)) and work out the equilibrium points of thesystem equations that are (0, 0), (0, 1), (1, 0), and (1, 1) based


N(0, 1) M(1, 1)

G

I

II

O(0, 0)W(1, 0)

(a)

(0, 1) (1, 1)

(0, 0) (1, 0)

(b)

Figure 9: The replication dynamic evolutionary phase diagram of the strategy interaction between enterprises.

on the equations 𝑑𝑝/𝑑𝑡 = 0, 𝑑𝑞/𝑑𝑡 = 0 when 𝑙𝐴𝜀𝐴> 𝑙1− 𝑠 −

{𝑞𝐶(𝑐1− 𝑘1) + 𝑔 + V + 𝛿[𝜂𝜙ℎ + 𝜂(1 − 𝜙)𝜑𝑚 + (1 − 𝜂)𝑚] + Δ𝑘},

𝑙𝐵𝜀𝐵> 𝑙2−𝑠−{𝑞

𝐶(𝑐2−𝑘2)+𝑔+V+𝛿[𝜂𝜙ℎ+𝜂(1−𝜙)𝜑𝑚+(1−𝜂)𝑚]+

Δ𝑘}. According to the matrix Jacobian characteristic valuetheorem, (0, 0), (0, 1), and(1, 0) are instability points; (1, 1) isevolutionary stable strategy (ESS). Figure 9(b) indicates thatthe systemwill converge to the ideal equilibrium statusmodel(𝐴1, 𝐵1) when it starts from any initial state. The proposition

is correct obviously.Therefore, increasing the discount value of the enterprise

future earnings can encourage the enterprises to cooperatein quality and safety. It indicates that enterprises 𝐴 and 𝐵should enhance mutual trust, establish long-term strategiccooperation partnership, andwork hard for creating excellentcooperation environment for the quality and safety in thefood supply chain.

4. Conclusions

This papermainly discusses two problems: firstly, the cooper-ation strategy for the quality and safety between the upstreamand downstream enterprises of the food supply chain and,secondly, the macro and micro factors that influence thecollaboration strategy for the quality and safety. The researchresults as follows:

(1) The food supply chain form that cooperates in boththe quality and safety and pricing can achieve thehigh-quality efforts efficiency and obtain high profitssimultaneously in the conditions of three kinds ofcooperation modalities, which are noncooperation,semicooperation, and cooperation.

(2) The interaction between the loss that the average qual-ity and safety events of per unit food caused each timeand the quality efforts marginal cost can influence

the upstream and downstream enterprises’ qualityefforts effectiveness. The loss that the food qualityand safety events caused has a vital impact on theenterprises’ quality efforts efficiency. There is a neg-ative correlation between the quality efforts efficiencyand the loss when the degree of quality efforts ishigher, and instead there is a positive correlationbetween them.

(3) The direct consequence of enterprises in pursuit ofmaximum profit is that they will reduce the totalinvestment in quality efforts. But increasing the dis-count value of the enterprise future earnings canencourage the enterprises to cooperate on quality andsafety and enhance mutual trust, establish long-termstrategic cooperation partnership, and work hard forcreating excellent cooperation environment for thequality and safety in the food supply chain.

Meanwhile, themacro environment will be the importantbasis for the enterprises’ decision-making on collaborationstrategy. The government should establish incentive andsupervision mechanism, and they also should increase thecompensation intensity for companies that carry out the qual-ity and safety efforts. The supervisory departments shouldstrengthen supervision on enterprises that do not carryout the quality and safety efforts, improve the supervisionefficiency, and appropriately punish them. The news mediashould disclose timely the enterprises’ behavior of not doingmore to carry out quality efforts and hurt their chances ofhitchhiking. However, excessive punishment can easily leadto the supervisory departments slacking off more and choos-ing the strategy that does not supervise enterprises.Therefore,the government should simultaneously strengthen supervi-sion and increase the punishing dynamics for the supervisorydepartments’ behavior, including the laziness behavior, theinaction behavior, and the power rent-seeking behavior.


The signal transmission which is about the quality andsafety of the food supply chain can realize the food qualityand safety information in two-way communication betweenenterprises and consumers, and it is beneficial to transformthe food quality and safety’s credence goods features intosearch goods features. Consumers can accurately distinguishthe level of food quality and safety and realize the separationbetween high-quality food production enterprises and low-quality food production enterprises; it also can encourageenterprises that do not carry out the quality and safetyefforts to increase investment in quality efforts and ultimatelyachieve the goal of improving the level of food quality andsafety progressively due to the reason that low-quality foodproduction enterprises cannot imitate the strong signal sentfrom high-quality food production enterprises. Consumersare willing to pay the price discrimination for the food whoselevel of quality and safety is high. The companies’ profits willincrease due to the increased consumer demands, thus fur-ther promoting enterprises to increase investment in qualityefforts. However, to explore how to improve the signal trans-missionmechanism and the path that can ensure the efficienttransfer of the signal to consumers is worth further analysis.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

The authors wish to express their gratitude to the refereesfor their invaluable comments. This work was supported bythe Major Program of National Social Science Foundationof China (no. 12&ZD204) and the National Natural ScienceFoundation of China (no. 71173103).

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