Matching Supply-Side Costs With Demand-Side Value in Procurement Auctions (Forthcoming in JoPP)

8/6/2019 Matching Supply-Side Costs With Demand-Side Value in Procurement Auctions (Forthcoming in JoPP)

1/27

MATCHING SUPPLY-SIDE COSTS WITH DEMAND-SIDE

VALUE IN PROCUREMENT AUCTIONS

Jeremy Chen

Decision Support SolutionsDefence Science and Technology Agency1 Depot Road, Singapore 109679, SingaporeE-mail: [email protected], [email protected]

Abstract: This paper presents a procurement auction format structuredso as to reconcile supply-side costs with demand-side value through thealignment of bidder and bid-taker interests. The existence of a dominantbidding strategy ensures this alignment and, at the same time,

discourages strategic bidding. The format also involves minimalrevelation of bidder information, making it attractive to bidders whoexpect continued participation in the same market.

Another major goal of this paper is to engage policy-makers through adiscussion of important issues, which were brought forth in the course ofdesigning and analyzing the aforementioned auction, that relate generallyto the successful execution of procurement auctions.

Keywords: auctions, bid evaluation, mechanism design

Biographical notes: Jeremy Chen is an Analyst in the Department of

Decision Support Solutions at the Defence Science and TechnologyAgency in Singapore. He earned his Bachelors degree in MechanicalEngineering at the National University of Singapore, and a Master ofScience degree in Computation for Design and Optimization at theMassachusetts Institute of Technology. His research interests includeoptimization, mechanism design, networks, stochastic control, andstrategic interactions between entities in supply chains.

INTRODUCTION

The tender evaluation process is often a complicated affair, involving the

comparison of bids on the basis of not only price, but also numerousspecifications, features, and factors relating to service or fulfillment. Thiscomplicated task essentially involves an evaluator computing a score foreach bid. Each score would, in turn, serve as a proxy to the value the


2/27

acquiring body (bid-taker) would expect to obtain from the associatedbid.

However, where a bidder lacks knowledge of how his potential customermeasures value, cases arise where a bid could be improved so as tosimultaneously provide a better value proposition for both bidder andbid-taker. Thus, where the procurement process fails to reconcile supply-side cost with demand-side value, inefficiency arises.

A possible solution would be for the bid-taker to provide bidders with thenecessary means to assess their own bids. This entails the codification ofbid-taker value into a metric for the valuation of bids, and the revelationof that metric. For example, when using AHP, it would correspond torevealing the hierarchy of assessment criteria, the weights, as well ashow each leaf criterion is assessed.

A natural concern would be whether such an approach would enablebidders to game the system and in doing so, cause a sub-optimaloutcome for the bid-taker. This leads us to the study of auctions.

Auctions1 of well defined items or contracts have bidder valuation as theunique strategic dimension and are essentially one-dimensional. On theother hand, procurement auctions typically involve a multitude ofcharacteristics and are inherently multi-dimensional.

The study of multi-dimensional auctions has had a relatively recenthistory. Thiel (1988) noted that given a procuring agency's preferences,the multi-dimensional procurement problem may be rendered one-

dimensional. Che (1993) studied design competition using a model oftwo-dimensional auctions with bids being evaluated under differentscoring rules and auction schemes. He was interested in rules andschemes where the firm with the lowest cost parameter would beselected. Branco (1997) studied the multi-dimensional procurementauctions with dependency among firms' costs. In that setting, he showedthat to implement the optimal outcome, a procurer will need to use a two-stage auction process where a bidder is selected in the first stage andbargaining (on quality) takes place in the second. However, Jap (2002)found that, in practice, suppliers offer their best prices through either astrategic sourcing process or a reverse auction but do not offersignificantly more value when the two are used together as in the case of

renegotiation.

1 See Soudry (2004) for an introduction and survey.


3/27

Auctions operate in the real world rather than in a one-shot academicsand box. Participants in an auction may interact repeatedly and/or mayhave the additional objective of deducing characteristics about othersfrom data revealed in the auction (Arora et al., 2007, Greenwald et al.,2010). Participants may also be concerned about cheating. These issuesarose during the course of the design and analysis of the auction and wehope our subsequent discussion of these matters will be useful to thepolicy-maker.

On the auction format itself, we aim to present a practical method forprocurement and enable readers to understand the economiccharacteristics of the auction. Mathematical proofs of are supplied inAppendix A so the interested reader may verify the assertions madeabout the auction.

Outline

In this paper, we propose a procurement auction mechanism that may beclassified as a best-value procurement method. We will first presentthe auction. Subsequently, we will discuss how aspects of our auctionmay make it attractive to practitioners. In particular, we discuss how itrelates to issues of cost structure revelation, bid-taker cheating andstrategic bidding on the part of bidders. We will also touch on theimportance, to the bid-taker, of being able to accurately articulate hervalue model. In Appendix A, we will characterize the optimal biddingstrategy and show that it is beneficial to the bid-taker and providemathematical justification for the value of knowing ones values.

Throughout this paper, the convention of using he to refer to biddersand her to refer to the bid-taker will be adopted. For brevity we willrefer to whatever the bid-taker is interested in procuring, whether a lot ofgoods, a service or a combination of both, as the good.

THE AUCTION

Preliminaries

We consider the procurement of a customizable good whosespecifications may be expressed as a string of real numbers (a vector in ). We assume that it is priced in terms of a positive real-valuedquantity (dollars), and that the bidders and the bid-taker (the acquiring


4/27

body) are risk-neutral (the marginal utility of each additional dollar isconstant).

It is assumed that higher benefits accompany higher specification levels.As buyers often have requirements that must be met, we shall assume thebid-taker will only accept specifications at least as good as a given level,. This defines a feasible region : for specifications2.Let denote the set of bidders making bids , where .The bid-taker measures the effectiveness of a good, given itsspecifications, using a benefit function . reports the dollar-equivalent of the benefit that accrues to her due to being furnished agood with specifications . Thus, may be viewed as a means ofquantifying value in dollars and cents. Thus, for a bid

, we define its

associated bid-taker utility, or net benefit,

, , as

, where is the price the bid-taker pays for a good with specifications .This is nothing but the benefit the bid-taker accrues over and above thecost of obtaining the good. We assume that procuring nothing generatesexactly 0 value for the bid-taker.

In the auction proposed below, the bidder that generates the highest netbenefit for the bid-taker wins the procurement auction. By disseminating, the bid-taker allows bidders to make use of this description of hervalue trade-offs3 to improve their bids.

We define the reserve net benefit, , to be stipulated by the bid-taker.We shall assume that 0. This value is analogous to reserve prices inauctions of well-defined items and represents the lowest net benefit thatthe bid-taker is willing to accept in the auction. This may arise as a resultof additional expenses associated with carrying out the transaction, or bean expression of market power.

2 The feasible region would typically be specified by shall-statements such asThe aircraft shall be capable of at least 3h of sustained flight on a full tank offuel; The radar shall be able to detect an object with a frontal RCS of 0.5m

2at a

distance of 10km or less. (Note that the latter statement may be described,equivalently, by the negative of the 0.5m2 frontal RCS detection range isgreater than -10km.)3 For a discussion of expressing value trade-offs, we refer the reader toHenderson and Hooper (2006), a delightful primer to decision theory.


5/27

On Quantifying Value

Tenders include descriptions of the criteria by which bids will beevaluated. Examples of criteria used include methodology proposed,track record, environmental issues, health & safety practices,management standards, support offered, and organizational fit. It will beuseful to consider an example.

The weighted sum of scores on different criteria is probably the mostcommonly used quantitative scoring method. This may be because it isintuitive to, separately, evaluate a bid on various criteria and thencombine the scores, accounting for the relative importance of the criteriaused. Such scoring functions take the form

where is the weight assigned to criterion , is the score of thebid with respect to criterion , and is the number of criteria.When using a scoring function in the above form, the determination ofweights for various criteria should be done such that they express, asaccurately as possible, the preferences of the bid-taking organization.There exist quantitative methods for doing so, for example the AnalyticalHierarchy Process (AHP) 4 (Saaty, 2001) and Swing Weights (Belton &Stewart, 2002, pp. 134-139).

Unfortunately, descriptions of some evaluation criteria often do not givebidders enough information to compute the score or net benefit of theirbids. While this problem can be addressed in some cases, there existevaluation criteria such as value as a national icon which may be

4 We highlight as an intuitive tool for weight determination that has been widelyused. AHP entails the use of pair-wise comparisons of the relative importance ofthe numerical scores associated with criteria to produce a set of weights and ameasure of the consistency of the aforementioned comparisons. While a set ofexpressed preferences inevitably exhibit inconsistencies, these can be reducedby careful examination of ones preferences. AHP may also be used iterativelyto generate a tree of criteria where criteria may be decomposed into componentsub-criteria. For details on the use of AHP, the reader is directed to Saaty (2001).

To represent value well, we emphasize that the pair-wise comparisons should bedone on the impact of numerical scores associated with criteria, instead of thecriteria themselves. This might be thought of as a synthesis of AHP and SwingWeights.


6/27

irreducibly qualitative. For the purposes of this paper, we consider onlyevaluation criteria that can be rigorously defined.

Note that, for the purposes of this paper, scores have to be converted todollars and cents. This necessitates assessing, at various (score) intervals,how much one values a good with a given score. If anything, this stephighlights that goods and/or services acquired should not cost more thanthey are worth.

The Auction Process

The market environment may be idealized as a setting where costs arethe private information of bidders. Thus, a bid-taker is precluded fromsolving a value maximization problem for each possible supplier andthen placing an order for a good of appropriate specifications herself.The difficulty and expense of acquiring accurate information aboutbidders' costs makes such a computation expensive and unreliable.Furthermore, even if costs are known bidders are unlikely to sell at cost,necessitating an additional, possibly lengthy, negotiation phase.

Consider an auction where the burden of solving bid optimizationproblems is shifted onto the bidders. They have a better picture of theircosts and can generate utility for themselves by winning the procurementauction with an appropriate bid.

The auction (Auction A) we propose may be described as follows:

1. The bid-taker reveals her benefit function, , to all bidders . This allows bidders to determine the net benefit, , ,that would accrue to the bid-taker given some bid ,.2. The value of is revealed to all, and bidders are given the option

of dropping out of the auction.3. If no bidders remain, the procurement process terminates and the

bid-taker does not buy anything.4. The bid-taker performs an English (ascending) auction5 on net

benefit beginning at . (This may be executed electronically.)5 The auctioneer starts a gradually increasing count

. In this case, the count is

of net benefit, and the starting value is . The net benefit rises in intervalsknown to all bidders. Bidders may voluntarily drop out of the auction and maynot return. By remaining in the auction, a bidder indicates his willingness tofurnish the bid-taker with a good at a price that will generate the a net benefit ofthe prevailing level of . This continues until only one participant has not


7/27

5. Denote the value at which the second-last bidder drops out to be

(if there is only one bid,

is

; if there is a tie,

is the

highest value at which the tied bidders are willing to supply thegood).

6. The last remaining bidder wins (given some tie breaking rule).Label him bidder . He must then announce a bid , thatgenerates a net benefit of to the bid-taker. (Naturally, mustmeet the bid-takers criteria for feasibility.)

7. Bidder supplies the bid-taker with a good/service withspecifications and is paid .

8. The auction process terminates. Other bidders do not supply thebid-taker anything (they produce at specification level 0) and arepaid nothing.

The key characteristic of this auction is the revelation of, a detaileddescription of how a (multi-dimensional) bid will be translated to a netdollar value (step 1). Based on this translation, the auction first followsthe well understood scheme of the English (ascending) auction (step 4).Once the bidder with the best value proposition for the bid-taker isidentified, he matches the winning value proposition with a detailed bidthat realizes that level of net benefit for the bid taker (step 6).

Suppose that the lowest price the winning bidder is willing to charge fora good with specifications is . By executing a transaction basedon the bid ,, he obtains more utility than if would have for the bid,

, which, without loss of generality, can be assumed to generate

nothing above his opportunity cost of executing the transaction.

An Example

Consider the following hypothetical market session viewed from thepoint of view of a single bidder, B, who wins the auction. Consider agood with some pre-defined specifications. Now, with that good in mind,suppose that the best net benefit that bidder B would be willing offer tothe bid-taker is $1M. This corresponds to some minimum price, $Pmin, heis willing to sell at. Suppose the starting net benefit is $0. Bidder Bwould stay in the auction as long as the prevailing net benefit is less thanor equal to $1M (see step 4). The longer other firms stay, the higher the

prevailing net benefit would be and the higher a net benefit bidder B

dropped out of the auction. In the event of a tie, some tie breaking rule will beused to select the winner.


8/27

would have to provide if he wins. A higher level of net benefitcorresponds to greater competition among suppliers which drives downthe cost of goods. Suppose the auction terminates at net benefit $0.75M.Bidder B then supplies a good of the previously mentioned specificationsto the bid-taker at a price that assures the bid-taker a net benefit of$0.75M. This means that bidder B is selling the good at $0.25M above$Pmin.

DISCUSSION: PROPERTIES OF THE AUCTION

Bidder Cost Structure Revelation

Firms generally avoid the revelation of costs as that amounts to the

minimum they are willing to accept for a good, information that might beused by others to their detriment in future transactions. Bidders inauctions are similarly wary of declaring the maximum amount they arewilling to pay for an item (their valuation of the item). This leads to theunpopularity of truthful auctions such as the Vickrey auction, where theoptimal bidding strategy is to bid their true valuation of the item.

As cost structure and the maximum price one is willing to pay for anauctioned item are analogous, let us consider the following example. InSingapore, the government leases large food centers by tender tointerested businessmen. These businessmen, in turn sublet stalls toindividuals who wish to sell food within these food centers. It is acommon practice for rentals to be raised for those operating relativelysuccessful stalls. In fact, concerted efforts are made at some food centersto accurately gauge the revenue of each stall, such as giving a smalldiscount to customers using cashless payment modes that allow thelogging of sales. Stallholders, in turn, make some effort to preventaccurate revenue estimation on the part of their landlords. Similarly,when continued interaction between buyer and seller takes place,information about ones valuation of an item is typically closely guarded.

Most market sessions in a reverse electronic marketplace feature aninformation revelation policy. The revelation policy determines theinformation (such as the number of competitors, the winning bids, etc.)that will be revealed to participating bidders at the beginning, during and

at the end of each market session. The information enables bidders toapproximate their opponents' cost structure, among other things.Accurate information about a competitors cost structure grant a firmsome advantages in strategic competition. Therefore, the choice ofinformation revelation policy has important consequences for the


9/27


10/27

Bidders are often aware of the possibility of cheating and are wary ofauction formats where cheating undetected is possible or easy. In fact,the New York branches of artwork auctioneers Christie's and Sotheby'shave previously admitted to bid running when the prevailing price is lessthan some secret reserve price (Rothkopf & Harstad, 1995).

The problem of shill bids is also present in our auction. Consider thefollowing scenario: A cheating bid-taker's shill will drop out of theauction at the same time as the last legitimate bidder, and the bid-takersown tie breaking rule would ensure that the shill is not awarded thetender. As a result, the winning bidder is paid less than he otherwisewould have been.

Transparency in the auction process is necessary to alleviate the fears ofbidders. Noting the role of the second-last remaining bidder in the

determination of the transaction price, the identity of the second-lastbidder might be made known at the end of the auction to verify that theprice was determined by a legitimate bidder.

Noting the foregoing discussion, transparency works at cross purposeswith the goal of bidders to maintain secrecy. However bidders in B2Bmarkets participate actively in sealed-bid auctions run by certain marketmakers such as Ariba even when bidders are merely informed of whetherthey have won and the price at which they won. The credibility of themarket-maker assures bidders that the auction is carried out with highstandards of integrity.

A bid-takers reputation for integrity may be such that bidders are willing

to forgo transparency to in favor of maintaining secrecy. (In the contextof this auction, the winning bidder reveals his full bid privately. Ifbidders are willing to vest more trust in the bid-taker, bidders mayannounce the maximum net-benefit they are willing to offer, allowing thebid-taker to automate step 4 of the auction process.)

Furthermore, credibility may not only alleviate fears of bid-takercheating, but also provide an incentive for bidders to willingly erodetheir profit margin where winning a tender has value in itself. (That is tosay, favorable prior evaluation by a credible evaluator may be anevaluation criterion in future auctions bidders wish to participate in.)This may occur in procurement auctions of big ticket items for which

verification of quality and effectiveness is difficult or requiresspecialized expertise. To quote a September 2003 article in the FinancialTimes by Spiegel & Wong (2003) on a tender for tactical-fighter aircraft(emphasis mine):


11/27

Much of the intensity is due to Singapore's reputation as

a ``reference customer'', one of a handful of countries

that carry weight because of the stringency and

transparency of their procurement process. For

companies with a new aircraft to market, winning the

Singapore contract would be a huge boost in the eyes of

other countries that may soon upgrade their air

forces,

Thus, bidders are sometimes willing to lower their prices as winning acontract with certain customers serves as a validation of a bidder'sproduct and boosts its estimated value in subsequent procurementauctions. This benefit can accrue to credible procurement agencies anddoes for Singapore as a buyer of defense materiel. In some respect, a bid-

taker reaping (value) benefits from her reputation may have too much tolose to cheat.

Bid-taker cheating is a concern that the format of Auction A alone cannotaddress satisfactorily. We submit that credibility is the answer to theissue of bid-taker cheating.

The (Positive) Effects of Strategic Bidder Behavior

The discussion of the effects of strategic behavior on the part of rationalbidders entails a commentary on the results established in the TechnicalAnnex (Appendix A). (It may be consulted if the reader is interested in

the mathematical development of these conclusions.)For Auction A, there exists a well defined (and simple) optimal biddingstrategy that is independent of the bidding strategies of the other bidders(see Proposition 11 in Appendix A). The consequence of this is thatbidders have no incentive to bid any other way if their objective is towalk away with as much utility as possible. (In the event that a bidder isnot interested in winning the auction but desires to merely obtaininformation about other bidders through their observable actions, it isarguable that private information is relatively well protected by thisformat.)

In addition, the auction is structured such that that bidder and bid-taker

interests are aligned. The optimal bidding strategy of any given bidder isto drop out only when the increasing net benefit exceeds that of the bestpossible offer he could make without charging below cost (see Corollary12 in Appendix A).


12/27

It follows from these properties that by revealing

to all bidders, far

from enabling bidders to game the system to the detriment of the bid-taker, using this particular auction format aligns bidder and bid-takerinterests by making a bidders winning the auction contingent on thevalue that he can provide.

The Value of Knowing Ones Values

In Value Focused Thinking, Keeney (1992) discusses the importance ofclarity on one's values in decision making. Considering an auction wherea bid-taker assesses bids in terms of a revealed value function, this ismost certainly the case. There is a cost associated with the lack of clarityon one's values. In this context, a bid-taker's lack of clarity on her values

results in the revelation of an inaccurate measure of value for the good,in turn resulting suboptimal bids from the point of view of the bid-taker.In this section, we seek to emphasize the need for rigor in thedevelopment of the measure of value to be used.

Failure in this respect can result in very poor outcomes for the bid-takeras described in a case by van der Hoek (2010). In the procurement oftransportation services for the disabled by a town in The Netherlands, thetender was evaluated on the basis of a proposed price schedule of sevenclasses of rides ranging from 100,000 to over 600,000 total rides. As thereal number of rides amounted to about 270,000, one of the biddersquoted high prices for the first, most relevant, classes and very low pricesfor the other classes. On the basis of all seven classes, he obtained thehighest score on the price criterion and won the contract. However, onthe basis of the real number of rides he was the second most expensivebidder of a total of five bidders. The town incurred avoidable costs to thetune of 36% of the amount tendered. If the agency in charge of thistender had greater clarity on the transportation needs of their town, theycould have ensured that the evaluation criteria better reflected the valueof a bid to their town.

In the case presented by van der Hoek (2010), the evaluation criteria wasa formula


13/27

min where is bidder s score, is the maximum score possible forcategory , is the price bidder quoted for category rides, is thenumber of categories, and is the number of bidders.It is notable that the winning bidder, consciously or unconsciously, tookadvantage of this evaluation criterion and played a dirty trick on theother bidders, and bid in a manner that depressed their scores on the lastfive categories8. Note that such tricks become impossible if bidder scoresare independent of each other9.

On the flip side, Waggener & Suzuki (1967) describe a case where valuedrove the outcome of large scale procurement of aviation fuel by theDefense Fuel Supply Center (DFSC). While there were many operationaland regulatory constraints in the selection of winning bidders, cost wasthe main driver of value. DFSC used least-total-cost as the criteria fordetermining which firms to select, as well as the means and routes ofsupply. Linear optimization was applied to determine the optimal (least-total-cost) solution out of the set of all possibilities that were feasible inan operational and regulatory sense. Further details on the methodologyused can be found in Waggener & Suzuki (1967) 10. Although the driverof value in this case is obvious, this example may still be used to

8 As a numerical experiment, we performed an ad hoc reweighting of the variouscategories such that it better reflected the towns demographic state and tookfuture demand growth into account. The vector of weights was changed to220,220,170,50,25,10,5 from the original 150,150,150,100,50,50,50. Ourreweighting ensured that the bidder proposing the cheapest schedule, as definedby present day demand, would have won by a clear margin on price. (Under theoriginal weights, the original winners score was 6.6% higher than that of themost cost effective option. Under the new weights, score of the most costeffective option is would have been 15% higher than that of the original winner,now in 3rd place, and 12.9% higher than the new 2nd placed bidder.)9 This is precisely the concept of independence of Irrelevant Alternatives (IIA)in elections. For IIA to hold, the relative ranking of two candidates must beunaffected by the entry of a new candidate. From this perspective, bid evaluation

and election systems are closely related. Readers may refer to Poundstone (2008)for an introduction to the theory of voting and elections.10 The first such procurement auction carried out by DFSC happened inFebruary 1961. Awards of $200,000,000 in jet fuel contracts were made to aboutfifty companies from among 100 companies submitting bids.


14/27

illustrate the possibility of obtaining an optimal outcome given a clearunderstanding of what provides value.

The cases above illustrate that the value of knowing ones values is notof mere illusory importance. By having clarity on what provides valueand making value an integral part of bid evaluation, one facilitates goodoutcomes in procurement. Conversely, a bid-taker that is unable to orotherwise does not correctly articulate her values can lose out if biddersbid strategically. This is formalized in Proposition 14 in Appendix A forthe particular context of the auction presented in this paper.

SUMMARY AND CONCLUDING REMARKS

In Auction A, bids are assessed purely on the basis of a pre-existingmodel of value possessed by the bid-taker and the auction formatminimizes the amount of unnecessary information revelation.Furthermore, far from allowing bidders to game the system, therevelation of a clear criterion for bid evaluation aligns the interests ofbidders with that of the bid-taker. We have also discussed the importance,to a bid-taker, of having clarity on what aspects of a good/servicegenerate value for her.

As an afternote to the discussion on Auction A, the bid-takers expectednet benefit can be maximized by judicious selection of. This followsfrom work by Myerson (1981) on optimal auctions. The process ofoptimally selecting

entails taking advantage of information on the costs

of bidders, and may be viewed as an assertion of information-basedmarket power. However, not only is cost information difficult to obtain,such optimization also damages trust and runs counter to good continuedbuyer-supplier relations. Thus, the optimization of bid-taker net benefitwas not pursued in this paper.

The auction we have presented is geared towards electronic execution.Being a new format, in implementation, it will face issues similar tothose faced by e-procurement methods. Within state governments, simplee-procurement innovations are more rapidly diffused than those that aretechnically or legally complex (Moon, 2005). Indeed, two of the criticalsuccess factors influencing success of e-procurement implementation areend-user uptake and supplier adoption (Vaidya et al., 2006). Thus,

comprehensibility and attractiveness are of foundational importance. Webelieve that the above auction presented is easily explainable and itsmechanics are similar to those in present day B2B auctions.


15/27

As with any procurement auction, bid-takers should make the effort tocarefully analyze, understand and, if possible, increase competitionamong suppliers participating in an auction. Strategic purchasingmeasures to increase the number of capable suppliers are, for instance,proper supply market research, global sourcing, as well as incentives forfuture supplier development. In fact, a study by Wagner and Schwab(2004) reports that the time firms spend to prepare for an ElectronicReverse Auction is positively related to auction success.

Even if one finds that the format of Auction A does not meet ones needs,one should take away the following: a successful procurement processrequires that one (a) understand how the product/service being procuredgenerates value for one, (b) articulate ones measure of value, and (c)assess bids based on that measure. This ensures the alignment of

incentives and increases the likelihood of a positive outcome.

REFERENCES

Arora, A., Greenwald, A., Kannan, K., & Krishnan R. (2007). Effects ofInformation-Revelation Policies Under Market-Structure Uncertainty.Management Science, 53 (8): 1234-1248.

Belton, V., & Stewart, T. J. (2002).Multiple Criteria Decision Analysis:An Integrated Approach. New York, NY: Springer Verlag.

Branco, F. (1997). The Design of Multidimensional Auctions. TheRAND Journal of Economics, 28 (1): 63-81.

Che, Y. K. (1993). Design competition through multidimensionalauctions.RAND Journal of Economics, 24 (4): 668-680.

Greenwald, A., Kannan, K., & Krishnan, R. (2010). On evaluatinginformation revelation policies in procurement auctions. InformationSystems Research, 21 (1): 15-36.

Henderson, D. R., & Hooper, C. L. (2006). Making Great Decisions inBusiness and Life. Chicago Park, CA: Chicago Park Press.

van der Hoek, M. P. (2010). Local Public Procurement: How to Dealwith a Creative Bidder? A Case Study from The Netherlands.Journal ofPublic Procurement, 10 (1): 121-135.

Jap, S. D. (2002). Online Reverse Auctions: Issues, Themes andProspects for the Future.Journal of the Academy of Marketing Science,30 (4): 506-525.


16/27

Keeney, R. L. (1992). Value-Focused Thinking: A Path to CreativeDecision Making. Cambridge, MA: Harvard University Press.

Milgrom, P. (2004). Putting Auction Theory to Work. New York, NY:Cambridge University Press.

Moon, M. J. (2005). E-Procurement Management in State Governments:Diffusion of E-Procurement Practices and its Determinants. Journal ofPublic Procurement, 5 (1): 54-72.

Myerson, R. B. (1981). Optimal Auction Design. Mathematics ofOperations Research, 6 (1): 58-73.

Poundstone, W. (2008). Gaming the Vote. New York, NY: Hill andWang.

Rothkopf, M. H., & Harstad R. M. (1995). Two Models of Bid-TakerCheating in Vickrey Auctions. The Journal of Business, 68 (2): 257-267.

Saaty, T. L. (2001). Fundamentals of Decision Making and PriorityTheory with the Analytic Hierarchy Process. Pittsburgh, PA: RWSPublications.

Soudry, O. (2004). Promoting Economy: Electronic Reverse Auctionsunder the EC directives on Public Procurement. Journal of PublicProcurement, 4 (3): 340-374.

Spiegel, P., & Wong, D. (2003). Defence top guns vie for a happylanding in Singapore: Several contractors' futures may hang on thecontest to supply the island nation. The Financial Times: 22 September

2003.

Thiel, S. E. (1988). Multidimensional Auctions.Economics Letters, 28:37-40.

Vaidya, K., Sajeev, A. S. M., & Callender, G. (2006). Critical Factorsthat Influence E-Procurement Implementation Success in the PublicSector.Journal of Public Procurement, 6 (1 & 3): 46-69.

Waggener, H. A, & Suzuki, G. (1967). Bid Evaluation for Procurementof Aviation Fuel at DFSC: A Case History. Naval Research LogisticsQuarterly, 14 (1): 115-129.

Wagner, S. M., & Schwab, A. P. (2004). Setting the Stage for

Successful Electronic Reverse Auctions. Journal of Purchasing &Supply Management, 10: 11-26.


17/27

APPENDIX A: TECHNICAL ANNEX

This annex covers the technical results underlying the claims made aboveabout our auction in the section on bidder behavior in the main text.

Bidder Utility

We previously defined bid-taker utility. Presently, we will define theutility of a risk-neutral neutral bidder (the marginal utility of eachadditional dollar is constant).

The benefit a bidder gets from a deal is the difference between what he ispaid for a product or service and the cost of supplying it. Let be thecost function for bidder . (A bidder being aware of his costs is no strongassumption as a well managed firm would have a clear understanding ofits business processes.) Bidder utility is thus

,, where is the price he is paid for supplying a good with specifications .Again, this is nothing but the amount paid to a bidder over and above thecost of supplying the good.

We will assume that a bidder who supplies nothing incurs no additionalcosts.

Describing Bidder Strategies

Let us now parameterize the manner in which bidders behave in AuctionA.

Definition 1 (Bidding Strategy). For Auction A, will be used to denotea bidding strategy. Bidders strategy , is said to be definedby the bid, .In words, for a bidder using the strategy , , is the lowest price heis willing to sell a good of that specification for.

In our subsequent analysis, we will use this to describe bidding strategies.

Define the highest net benefit that bidder

is able to provide as


18/27

,

.

During step 4 of Auction A, bidder stays in the auction until the prevailing net benefit exceeds . If he wins, he announces the bid, which exactly attains the benefit level .The Outcome of Auction A

From the point of view of bidder , the highest valued bid other biddersare willing to make is essentially exogenously given. (He may interpret itas a random variable.) Denote it

max , max\ .First, we show that if bidder wins the auction, this gives the value of.Lemma 2 (Second Highest Net Benefit). In Auction A, followingDefinition 1, if bidder wins the auction,

.Proof: The result follows immediately from Definition 1, steps 4 and 5.

We now establish the intuitive fact that rational bidders will not adopt astrategy that may cause them to sell below cost.

Lemma 3 (No Bidding Below Cost). In Auction A, following Definition1, for any bidder, the utility accruing from any strategy , where , is dominated from that which would accrue from the strategy,.Proof: First, we say that could win if he is in first place or tied forfirst place in terms of net benefit (see step 4).

If loses the Auction A with the strategy ,, he would also lose theauction using

,as

, , (see step 4).

For the same reasons, if could win the auction with the strategy,, he could also win the auction by using ,. Furthermore,the utility accrued in both cases would be the same by step 5, step 6 andDefinition 1.


19/27

In the case where

could win the auction with

,, but loses the

auction when using

, , it follows that

.

Suppose he wins the auction using , and announces a price .Since, , this implies that . Hence, , 0.Thus, in no case can a strategy , , where , produce abetter outcome than a strategy , . This proves the result. We now proceed to touch on the utility that accrues to the winningbidder and bid-taker, following which we describe the total surplus dueto a transaction taking place.

Lemma 4 (Bidder Utility). In Auction A, following Definition 1, ifbidders are rational, losing bidders garner a utility of 0, and the winning

bidder, , accrues utility ,, which satisfies,, 0.Proof: The resulting value for losing bidders follows from step 8. By

Definition 1, . Step 7 tells us that, , .

By Lemma 2 and the assumption of rationality, , thus,

,

. Step 5 informs us that

0. This

concludes the proof. It follows from the above that bidders have nothing to lose byparticipating in the auction.

Corollary 5 (Ex-post Individual Rationality). The auction mechanism isex-post individually rational.

Proof: The result follows from Lemma 4. In practice however, the costs of making a bid are non-negligible.However, as the bid-taker reveals , the research costs of the bidderare reduced to (mainly) studying his own production and opportunitycosts.

Next, we touch on the utility that a bid-taker obtains.


20/27

Lemma 6 (Bid-taker Utility). In Auction A, following Definition 1, if nobidder is selected, the bid-taker's utility is 0, but if there is a winner,

bidder, her utility is given by, 0.Proof: The result follows immediately from step 7 and the assumptionthat 0. It turns out that the surplus due to trade depends only on the Measure ofEffectiveness the bid-taker has for the good and the cost structure of thewinning bidder. We proceed now to establish this result.

Lemma 7 (Surplus due to Trade). Let

be the total utility of all

bidders and the bid-taker. In Auction A, following Definition 1, if no

bidder is selected, 0. On the other hand, if there is a winner,bidder, , .

Proof: It is clear that total utility is 0 if the auction concludes with nowinner. Consider, now, the case where there is a winner, bidder .The proof of Lemma 4 gives an expression for the utility of a winningbidder. Along with Lemma 6, we obtain

.

Since , , , .

This concludes the proof. Lemma 7 implies that as long as bidder wins, he and the bid-takershare a fixed amount of utility. Intuitively, this is shared on the basis ofmarket-power. The bid-taker is guaranteed in value, which is equalto the net benefit of her best alternative to bidder

s bid. Bidder

must

concede this much value to the bid-taker, otherwise the bid taker will nottransact with him. In a competitive market, the bid-taker has highervalued alternatives and is thus able to secure a larger fraction of thetrade-surplus.


21/27

Bidder Behavior, Optimal Bidding and its Implications

The set of bids that a rational bidder would be willing to make and havenet benefit at least may be defined to be

, : , , , or equivalently,

, : , , 0.Note that Lemma 3 has been used in this definition. Recall that a strategy

, defined by a bid

, ensures that if the bidder using that

strategy wins, the utility that accrues to him is at least that which isobtainable if he was paid to supply a good with specifications . Thisis implied by Definition 1.

Denote the set of specifications associated with the set to be : , .It follows that bidder may rationally use a winning strategy (or one thatties for a win) if the set is non-empty.We now proceed to characterize the optimal bidding strategy for

. But

prior to that, to be clear on nomenclature, let

arg max denote the subset of where the function attains its maximum.Proposition 8 (Maximum Net Benefit). In Auction A, following Definition 1, if , then the bidder 's bid-taker utilitymaximizing bid is some , where arg max .Proof: If is a singleton then we are done. Otherwise, the bid thatmaximizes bid-taker utility (net benefit to the bidder) lies in


22/27

arg max, p

where x, p: , with the conditions for setmembership following from the feasibility of bids and rationality of the

associated bidding strategies (Lemma 3). We aim to show that ,belongs to this set.

First note that , satisfies the rationality constraint. Now supposethat there exists a bid , such that

.The rationality of using the strategy , implies that y .We also deduce that , , otherwise the bid will generateless bid-taker utility than , so .This contradicts the definition of , , therefore no such bid, can exist. Therefore, ,, and we have proven theresult. Lemma 9 (Monotonicity). In Auction A, following Definition 1, the probability of bidder

winning the auction using the strategy

, is monotone non-decreasing in bid-taker utility,, .Proof: The bidding strategies of the other bidder define the respective 's. Thus, bidder 's probability of winning is similar to a step function:

wins using , 0 , , 1 ,

where

0,1depends on the tie-breaking rule used.

Therefore, given any probability distribution on the other bidders' costfunctions and bidding strategies, a bidder 's probability of winning theauction using the strategy , is monotonically increasing in, .


23/27

This result leads to the following corollary.

Corollary 10 (Maximum Probability of Winning). In Auction A, following Definition 1, if , then the strategy that maximizesbidder's probability of winning is some , where arg max .Proof: The result follows immediately from Lemmas 8 and 9. We are now able to describe the optimal bidding strategy of bidders.

Proposition 11 (Optimal Bidding Strategy). In Auction A, following Definition 1, if , then the bidding strategy that maximizesbidder

's expected utility is some

,where

arg max .On the other hand, if , bidder's utility is expected maximizedat the value 0 (not winning) and is attainable by using any bidding

strategy ,.Proof: If , bidder is unable to simultaneously win theauction and obtain non-negative utility. The maximum utility he mightobtain is then 0, and may be attained with any (losing) bidding strategy

of the form ,.Consider the case where

. A strategy associated with a bid

within would garner non-negative utility, which dominates thealternative of using a strategy associated with a bid outside (garnering non-positive utility). Thus, the optimal bidding strategy is, for some , in .In doing so, bidder 's expected utility, given a bidding strategy , ,is

wins using , , , wins using , By Lemma 6, the bid-taker's utility will be given by

. So,

. Thus, the expected utility bidder would get, given a bid , ,would be


24/27

wins using ,

Note that

arg max arg max .Since, max max max ,we may use Corollary 10 to conclude that bidder maximizes theexpected utility he would get by selecting some strategy with

arg max as the specification component of his bid and as the pricecomponent.

This completes the proof. As a point of note, if is concave and is convex, is concaveand will be a convex set. This has positive implications for biddersusing computational methods to determine an optimal bidding strategy. If,in addition, is strictly concave, the optimization problem has aunique optimum.

The intuition for these results is further developed in Figure 1 (where the

bidder index has been dropped). In Figure 1, only a single specification,Quality is considered, but this suffices to provide the requisite intuition.

Three indifference curves for the bidder (SIC1-3) are shown with theircorresponding utility levels. The curve , defined by corresponds to the indifference curve which grants 0 utility (SIC1).Three indifference curves for the bid-taker (BIC1-3) are shown with theircorresponding bid-taker utility levels. For the bidder, higherindifference curves provide more utility; for the bid-taker, lowerindifference curves provide greater utility.

Suppose that the best bid of the bidders other than is valued at 0.5

(corresponding to some point on BIC3). Bidder

may then place a

bid anywhere in 0.5 to win or be a possible winner. The utilityhe will accrue from winning the auction will then be the differencebetween the value of his bid and 0.5. From Figure 1, we see thathe may achieve this by finding the level of ``Quality'' and price that


25/27

maximize the difference between BIC3 and SIC1 which is an intersectionbetween his cost curve (SIC1) and (BIC2).

Having characterized the optimal bidding strategy, it is now clear that theoptimal bidding strategy has positive implications for the bid-taker aswell:

Corollary 12 (Optimal Bidding is Favorable to the Bid-taker). In Auction A, following Definition 1, the bid defining bidder 's utilitymaximizing strategy maximizes over.Proof: This follows from Propositions 8 and 11. In the foregoing discussion, we have established that optimal bidding onthe part of bidders is favorable to the bid-taker. As such, the revelation of

to all bidders does not hurt the interests of the bid-taker.

Figure 1. Bidder and Bid-taker Indifference Curves and Optimal Bidding


26/27

The Value of Knowing Ones Values

Now we establish the fact that a bid-taker should be clear on how shederives value from a good before revealing to bidders. Otherwise sherisks avoidable losses due to this lack of clarity. A more detaileddiscussion on this is available in the main text.

Lemma 13 Suppose a bid-taker ran auction A, revealing instead ofand that all bidders acted rationally. The (true) utility that she would

accrue from any bidder's bid is never more than the (true) utility shewould accrue from bidder's bid resulting from her revealing .Proof: Consider Propositions 8 and 11. A bid made under an incorrectrevealed Measure of Effectiveness may satisfy the constraints ,but by the optimality of the bid made under correct revelation of

,

which maximizes bid-taker utility, it cannot generate greater utility forthe bid-taker. Proposition 14 (The Value of Knowing One's Values). Suppose a bid-taker ran auction A, revealing instead of and that all bidders actedrationally. Her resulting (true) utility from the auction is dominated by

the (true) utility she would have gotten should she have revealed.Proof: We say a strategy is has a net benefit of at least if the biddefining the strategy has a net benefit of at least .Let be the set of bidders bidding with strategies with net benefits of atleast in an auction where was revealed. By Lemma 13, the resultingbids of all bidders remain constant or are reduced in value. We consider

the following cases:

If|| 0, the bid-taker accrues no utility from the auction and cannotdo better.

If|| 1, the bid-taker obtains at most in utility from the auction andcannot do better.

If|| 2, a number of possibilities arise. Without loss of generality, letthe original top bidder be bidder 1 and the runner-up be bidder 2. If thenet benefit of bidder 1's strategy falls below that of bidder 2, the bid-taker's utility is strictly reduced. If the net benefit of bidder 1's strategydoes not fall below that of bidder 2, the bid-taker's utility is eitherreduced or stays the same, depending on whether the net benefit ofbidder 2's strategy falls. Thus, the proof is complete.


27/27

To make this clear, Figure 2 illustrates the result of revealing an incorrect

. Incorrect revelation is shown using two indifference curves

and

that deviate from the true curve . Both lead to suboptimal bids.

Figure 2. Truthful Buyer-taker Value Revelation is Optimal

Documents

Matching Supply-Side Costs With Demand-Side Value in Procurement Auctions (Forthcoming in JoPP)