AVOIDING THE COLLUSION AMONG THE BIDDERSAND THE AGENT IN SEALED-BID AUCTIONS1Şevket Alper KOÇ Kocaeli University ABSTRACT We study an auction in which bidders can bribe the auctioneer before they bid and before they know the identity of the winner, with the auctioneer lowering the winner’s bid if the winner is bribed. We show that, in second-price sealed-bid auctions, given the size of the bribe set by the auctioneer, none of the bidders do pay the bribe and every bidder bids his valuation. We also show that the revenue equivalence theorem breaks down when there is bribery because the proposed corruption does not work in the second-price sealed-bid auctions. The first-price and second-price auctions do not yield the same expected revenue to the seller. Keywords: Auction, Auctioneer, Bribe, Bidders Corruption.1. INTRODUCTIONIn many cases, but not all, a sealed-bid auction has an auctioneer. Sometimes the auctioneer is a third party in the transaction, and sometimes it is an individual who works for the firm awarding theprize and who is given the task of collecting the bids from the bidders.The existence of an agent coming between the seller and the biddersraises the possibility of corruption. One of the ways that corruptionoccurs is that the auctioneer could look at the submitted bids and thensolicit a bribe from the winner after the bids are submitted in exchangefor changing the bid in a way that is favorable to the winner. In astandard high-bid auction, this would entail soliciting a bribe in exchangefor lowering the winner’s bid down to the second-highest bid. Severalexisting papers address ex post bribery that occurs after all of the bids are 1 I am indebted to William Neilson, Thomas Jeitschko and Wolfgang Köhler for their helpful comments.Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

Avoiding The Collusion Among The Bidders and the Agent… 259submitted.2 Another way that corruption occurs is that the auctioneercould solicit bribes from the bidders before the bids are submitted3, inexchange for a promise to reduce the bidder’s bid should that bidder bethe winner. Koc and Nielson (2005) construct a model to fit this feature.The auction is a first-price sealed bid auction with no reserve price, withthe high bidder winning and paying the second-highest bid. Before thebidding, the auctioneer announces the size of the bribe he demands. Asmany bidders as want to can pay the bribe, and if a bidder who pays thebribe submits the highest bid, the auctioneer lowers the winning bid tothe second-highest bid.4 The high bidder then wins the auction and paysthe second-highest bid. In this case, in equilibrium, only bidders withvaluations higher than some critical value pay the bribe. Corruption hasno effect on either efficiency or the bidders’ expected payoffs when thebidders are symmetric5.Koc and Neilson (2005) shows that in the case where all bidders drawtheir valuations independently from a single distribution, bidders whohave valuations higher than some critical value pay a bribe to theauctioneer, and bidders with low valuations do not. Bidders who pay thebribe bid their own valuations as if they were in a second-price sealed-bid auction, and bidders who do not pay the bribe bid according to thestandard equilibrium bid function from the first-price auction. Theresulting bid function for all bidders is increasing, and therefore thebidder with the highest value wins the auction, whether he pays the bribeor not, and the auction is efficient. The bidders’ expected equilibriumpayoffs are unaffected by corruption. They are neither worse off nor2 Lengwiler and Wolfstetter (2000) analyze auctions in which the winning bidder can bribe the auctioneer tochange the bid after the auction has ended. Their results are similar to ours, although the results depend on thepossibility of the corruption being detected and punished. Menezes and Monteiro (2001) consider a scenarioin which there are two bidders and the auctioneer approaches one of them to solicit a bribe in return forchanging the bid. The auctioneer can approach either the winner or the loser. Burguet and Perry (2000) studyan auction in which one bidder is honest but one is corrupt. Burguet and Che (2004) and Celentani andGanuza (2002) study a procurement auction in which the awarding of the contract is based on both the priceand the quality of the project, and a corrupt auctioneer can manipulate the quality component in exchange fora bribe.3 Corruption can also arise through bidding rings, in which the bidders collude to increase their surplus fromthe seller. See, for example, Graham and Marshall (1987), McAfee and McMillan (1992), and Marshall andMarx (2002). Comte et al. (2000) link the bidding ring literature and the bribery literature with a model of expost bribery in which the bidders use corruption to enforce collusive behavior.4 We ignore issues related to the credibility of the auctioneer’s promise, assuming instead that the promise isenforceable. Credibility might occur, for example, if the auctioneer makes this promise repeatedly in auctionsover time, so that reputational concerns cause the auctioneer to keep the promise.5 See Koc and Nielson (2005).Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

260 Avoiding The Collusion Among The Bidders and the Agent…better off in terms of the equilibrium expected payoffs. However, there isa transfer of wealth from the seller to the auctioneer. In second-pricesealed-bid auctions collusion agreement between the bidders is easier tosustain than in first-price sealed-bid auctions. As Robinson (1985) shows,if there are no problems in coming to agreement among all bidders andabstracting from any concerns about detection, etc., the optimalagreement in a second-price auction is for the designated winner to bidinfinitely high while all the other bidders bid zero. No other bidders haveany incentive to cheat on this agreement. But in a first-price auction thebidders have to agree that the designated bidder bid a small amount whileall the other ones bid zero. In this framework, most of the bidders thenhave a substantial incentive to cheat on the agreement.6However, for the issue of corruption between the auctioneer and thebidders, the scenario is different. In this scenario, corruption takes thefollowing form. The auctioneer approaches the bidders and tells themthat if they pay a bribe of a certain amount and if they submit the highestbid, the auctioneer will change their bid so that they only have to pay thesecond-highest bid. But, in second price auctions bidders have dominantstrategy. They bid their values no matter what the other bidders do andpay the second highest bid anyway if they win. Hence, the sealed-bidsecond price auctions are not vulnerable to the proposed corruptionscheme that involves the auctioneer and the winning bidder because theyalone cannot change the price. They also need the collaboration of thesecond highest bidder to pull the price down to the third highest bid.7 So,the bidders do not accept the offer made by the auctioneer, in other wordsthey do not pay the bribe to the auctioneer. All they do is to play theirdominant strategy and bid their value.This paper is not simply an academic exercise, because ex ante briberyhas been documented in actual auctions. In their bids for corporate waste-disposal contracts in New York City, Mafia families would sometimespay bribes for an “undertaker’s look” at the bids of the other biddersbefore making their own bids.8 In 1997 a Covington, Kentucky,developer was shown the bids of two competing developers for a $376 Milgrom (1987) develops a similar intuition to argue that repeated second-price auctions are more vulnerableto collusion than repeated first-price auctions.7 See Lengwiler and Wolfstetter (2000).8 Cowan, R. and D. Century, Takedown: The Fall of the Last Mafia Empire, (New York: G.P. Putnam’sSons.2002), s. 223-231.Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

Avoiding The Collusion Among The Bidders and the Agent… 261million dollar courthouse construction project.9 In Chelsea,Massachusetts, in the 1980s, the city’s auctioneer was accused ofaccepting bribes to rig auctions in favor of certain bidders, one timeserving as a bidder’s agent in an auction he was running.10 Lengwiler andWolfstetter (2000) relay two examples involving German firms whichthey claim provide evidence of ex post bribery, but we think providebetter evidence of ex ante bribery. In one incident, one bidder illegallyacquired the application documents of a rival bidder for the Berlin airportconstruction contract, and in a second incident, Siemens was barred frombidding in public procurement auctions in Singapore for five yearsbecause they had bribed an official for information about rival bids.Since the rival bids could be obtained and used before the bribers madetheir own bids, these could be instances of ex ante bribery.Finally, we have also been told that auctioneers solicit ex ante bribes forsome types of procurement contracts in Turkey. The contracts areauctioned using a standard first-price sealed-bid auction, with the bidderwho offers to supply the good at the lowest price winning the auction andsupplying the good at that price. Before the bidding starts, the corruptauctioneer approaches certain bidders with whom he has worked before,and offers to raise their bids to the second-best bid if they win inexchange for a bribe.11This paper analyzes that the seller can avoid the ex ante bribery thatoccurs before the bids are submitted in sealed-bid auctions by requiringsecond-price auctions. We show that, in second-price sealed-bid auction,given the size of the bribe set by the auctioneer, none of the bidders dopay the bribe and every bidder bid his valuation. This is because thebidders pay the second highest bid instead of their bids. There would beno advantage for them to pay the bribe. As a result, by requiring theauctioneer to run a second-price rather than a first-price auction, theseller can avoid the revenue loss caused by a corrupt auctioneer.We also show that the revenue equivalence theorem breaks down whenthere is bribery issue because the proposed corruption does not work in9 Crowley, Patrick, Bid Scandal Bill in Trouble, (Cincinnati Enquirer, January 21, 2000).10 Murphy, Sean P, Chelsea Businessman is Said to Allege Attempted Bribery, (Boston Globe, September 22,1993).11 Ingraham (2000) uses empirical methods to study bidder-auctioneer cheating in sealed-bid auctions. Basedon statistical properties of the bids, he develops a regression method for analyzing potential cheating of thistype. He applies this regression specification to data from the New York City School Construction Authorityauctions, and finds evidence that there is cheating between the auctioneer and the bidders.Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

262 Avoiding The Collusion Among The Bidders and the Agent…the second-price sealed-bid auctions. The first-price and second-priceauctions do not yield the same expected revenue to the seller.We proceed as follows: in section 2, we present the game and thenotation. Section 3 examines the behavior of the bidders and theauctioneer. Section 4 characterizes the revenue equivalence theorem andshows how it breaks down. Section 5 concludes the discussion.2. STRUCTURE OF THE GAMEThere is a seller of a single good who faces n risk neutral potentialbuyers. The seller has hired an auctioneer to run a sealed-bid second-price auction, and pays the auctioneer a fixed wage (as opposed to acommission) in exchange for his services.12 In contrast to the standardsecond-price auction, the game is supplemented by corruption betweenthe auctioneer and the bidders. The auctioneer approaches every bidderbefore the auction is held and tells them that if the bidder agrees to pay abribe of , and is the highest bidder, he pays the second-highest bid. Ifthe highest bidder did not pay the bribe, he pays his bid. Bribes arecollected from all bidders who agreed to pay, even from losing bidders.Consequently, the game is a 3-stage game. In the first stage theauctioneer sets , in the second stage the bidders decide whether to pay independently and simultaneously, and in the third stage the bidderschoose their bids.The bidders’ valuations v1,...,vn are independently and identically drawnfrom the distribution F with support 0,1, with a density f, as in thestandard symmetric private values model. We assume that the value ofthe object to the seller is zero and the reserve price is zero. There is noentry fee, making it optimal for all bidders to bid. The seller is passive inthis game and we ignore issues related to the detection and punishment ofcorruption.We restrict attention to equilibria that survive weak dominance. Thisrules out preemptive strategies such as one bidder paying the bribe andbidding above 1 while the other bidders do not pay the bribe and bidzero.12 In the U.S., at least, many auctioneers are paid a commission based on the sales price. Such a paymentscheme may reduce the auctioneer’s incentives to solicit bribes, but that issue is left to future research.However, when a firm assigns the task of collecting bids to one of its employees, so that the employee is theauctioneer, that employee is rarely paid a commission.Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

Avoiding The Collusion Among The Bidders and the Agent… 263As is well known, the unique symmetric equilibrium of the second-price auction is the profile of strategies 1,..., n such that all i ’s are equaland all i ’s are best responses for i given the strategies of all otherbidders. This unique symmetric equilibrium strategy is given by,b2 vi vi . (1)3. BIDDER AND THE AUCTIONEER BEHAVIORIn this section we start with the analysis of the behavior of bidders giventhe size of the bribe, , set by the auctioneer in first-price auctions.Specifically, we characterize the equilibrium of the subgame that followsthe auctioneer’s choice of . The first task is to find the bids of bidderswho do and do not pay the bribe. If a bidder pays the bribe and is thehighest bidder, he pays the second highest bid. Therefore, after payingthe bribe the bidder essentially participates in a second price auction, andhis dominant strategy is to bid his valuation.Lemma 1: Any bidder who pays the bribe bids his valuation, vi.Our main result concerns when bidders pay the bribe and when they donot. The next lemma states that bidders use cutoff strategies, that is, forbidder i there is a valuation vi* such that he pays the bribe when vi ≥ vi*and does not pay the bribe when vi < vi*.Lemma 2: In any equilibrium every bidder uses a cutoff strategy.Proof: See AppendixHowever, in a second-price auction no matter what the other bidders do,bidder i has a dominant strategy: he bids his valuation, vi . As a matterof fact a bidder, regardless of he pays the bribe or not, bids his valuation.Hence, he does not have incentive to collaborate with the auctioneer andas a result he will not pay any positive amount of bribe.Theorem 1: Given the amount of the bribe , there exists a uniqueequilibrium in which bidders with values in [0,1] do not pay the bribeand bid their valuation.Proof: Bidders have dominant strategy in second-price auctions; they bidtheir valuation. Consider bidder i with valuation vi . If he does not paythe bribe he bids vi and if he wins he pays the second highest bid, whichwould be v2 . Then, his profit would be vi v2 . If he pays the bribe heYönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

264 Avoiding The Collusion Among The Bidders and the Agent…bids his value and if he wins he pays v2 . This tine his profit would bevi v2 . As long as bribe is positive bidder i doesn’t pay the bribe.In the first period the auctioneer chooses the size of the bribe that abidder must pay in order to learn the second highest bid if he is thehighest bidder. So, the auctioneer aims to maximize his expected revenueby choosing . By Theorem 1, though, for any given , bidders do notaccept to pay the bribe to the auctioneer. Therefore, the auctioneer isindifferent about the size of the bribe.4. BREAKDOWN OF REVENUE EQUIVALENCE THEOREMAs stated earlier the proposed corruption does not work in the second-price sealed-bid auctions and as a matter of fact, the revenue equivalencetheorem breaks down. The first-price and second-price auctions do notyield the same expected revenue to the seller.According to the revenue equivalence theorem, when each of a givennumber of risk neutral potential bidders of an object has a privatelyknown value independently drawn from a common, strictly increasingdistribution, then any auction mechanism in which (i) the highest valuebidder always wins the auction, and (ii) any bidder with the lowestfeasible value expects zero payoff, yields the same expected revenue tothe seller and results in each bidder making the same expected payoff asa function of his value.13Koc and Neilson (2004) show that the first-price auction is still efficientand the auction awards the prize to the highest bidder and in equilibrium,bribes are a transfer from the seller to the auctioneer. Although briberychanges the bid functions of some bidders, namely those with sufficientlyhigh valuations, it has no effect on the final allocation of the prize or thewelfare of the bidders. From the standard auction theory we know that inthe first-price auctions and second-price auctions the expected payoffs ofthe bidders are identical. As a result, bribery does not affect the expectedpayoffs of the bidders in two different auctions; they both yield the sameexpected payoffs to the bidders.But in terms of the expected revenue of the seller, in the first-priceauction with bribery it is the expected value of the second highest valueminus the expected revenue of the auctioneer, which is13 See Klemperer (1999).Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

Avoiding The Collusion Among The Bidders and the Agent… 265Ev2 n1 F v* v* (2) where n is the number of bidders, 1 F v* is the probability that a given bidder pays the bribe, and v* is the size of the bribe. In thisequation first term is the expected revenue of the seller in the absence ofbribery in first or second-price auctions; the second term is theauctioneer’s expected revenue. Koc and Neilson (2004) show that thisexpected revenue of the auctioneer is strictly positive in first-priceauction. On the contrary, the seller’s revenue in the second-price auction with bribery is E v2 because the second term is zero. Hence, revenueof the seller is strictly greater in the second-price auction than in the first-price auction.This is an important result that when we introduce the bribery into themodel, the revenue equivalence theorem fails.5. CONCLUSIONIn this paper we analyzed a model of bribery in sealed-bid auctions. Thebribery involves the auctioneer, who acts as an agent on behalf of theseller, and the bidders. Our results show that, given the size of the bribeset by the auctioneer, none of the bidders do pay the bribe and everybidder bid his valuation if the auction is standard second-price sealed-bidauction. This is because the bidders pay the second highest bid instead oftheir bids. There would be no advantage for them to pay the bribe. As aresult, by requiring the auctioneer to run a second-price rather than afirst-price auction, the seller can avoid the revenue loss caused by acorrupt auctioneer.We also show that the revenue equivalence theorem breaks down whenthere is bribery issue. The first-price and second-price auctions do notyield the same expected revenue to the seller.Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

266 Avoiding The Collusion Among The Bidders and the Agent…APPENDIXProof of Lemma 2: Fix any equilibrium and consider the (right-continuous) cdf, Gi(b), of the highest bid of bidders j ≠ i. Also let xi(b)denote the probability of i winning with bid b against the rival biddersemploying their equilibrium strategies. (Note that xi(b) may not equalGi(b) since a tie may arise at a mass point b.) Let Bc be the set of b’s forwhich G is continuous, and let Bm be the set of b’s for which G jumps.Then Uic (v) (v b)dGi (b) (v b)[Gi (b ) Gi (b )] . b v ,bBmb v ,bBcUic(∙) is absolutely continuous and can be rewritten asvUic (v) Gi (s)ds Uic (v' ), (A1)v'for any v’.Now considerUin(v) = supb(v − b)xi(b).It follows thatUin(v) = maxb(v − b)Gi(b),since (v − b)Gi(b) is an upper envelope of (v − b)xi(b). One can check thatUin(v) is absolutely continuous, that the maximum is well defined (sincean upper envelope is upper semicontinuous and the choice can be boundto a compact set without loss of generality), and that f(b,v) := (v − b)Gi(b)is differentiable in v for every b in the equilibrium support. Hence, onecan invoke Theorem 2 of Milgrom and Segal to show that v (A2)Uin (v) Gi (b* (s))ds Uin (v' ),v'for b* (s) argmaxb(v − b)xi(b).It follows from (A1) and (A2) that vUic (v) Uin (v) [Gi (s) Gi (b* (s))]ds [Uic (v' ) Uin (v' )]. (A3) v'Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

Avoiding The Collusion Among The Bidders and the Agent… 267Since b*(s) < s for almost every s, it is clear from (A3) that, wheneverUic(v') − Uin(v') > 0, it must be that Uic(v) − Uin(v) > 0 for v > v', whichproves that the equilibrium strategy must involve a cutoff strategy withsome threshold vi*.REFERENCESBurguet, R. and Y.K. Che (2004) “Competitive Procurement withCorruption”, Rand Journal of Economics, 35, 50-68.Burguet, R. and M. Perry (2000) “Bribery and Favoritism by Auctioneersin Sealed-Bid Auctions”, working paper, Rutgers University.Celentani, M. and J.J. Ganuza (2002) “Corruption and Competition inProcurement”, European Economic Review, 46, 1273-1303.Comte, O. A. Lambert-Mogliansky and T. Verdier (2000) “Corruptionand Competition in Public Market Auctions”, working paper, CERAS-ENPC, CNRS.Cowan, R. and D. Century (2002), Takedown: The Fall of the Last MafiaEmpire, New York: G.P. Putnam’s Sons.Crowley, P. (2000) “Bid Scandal Bill in Trouble”, Cincinnati Enquirer,January, 21, 2000.Graham, D.A. and R.C. Marshall (1987) “Collusive Bidder Behavior atSingle Object Second-Price and English Auctions”, Journal of PoliticalEconomy, 95, 1217-1239.Ingraham, A. (2000) “Testing for Cheating Between Bidders andAuctioneers in Sealed-Bid Auctions”, working paper, University ofMaryland, College Park.Klemperer, P. (1999) “Auction Theory: A Guide to Literature”, Journalof Economic Surveys, 13, 227-286.Koc, Ş.A. and W.S. Neilson (2005) “Bribing the Auctioneer in First-Price Sealed-Bid Auctions”, working paper, Texas A&M University,College Station.Lengwiler, Y. and E. Wolfstetter (2000) “Auctions and Corruption”,working paper, Humboldt-Universitat zu Berlin.Marshall, R.C. and L. Marx (2002) “Bidder Collusion”, working paper,Penn State University.McAfee, R.P. and J. McMillan (1992) “Bidding Rings”, AmericanEconomic Review, 82, 579-599.Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

268 Avoiding The Collusion Among The Bidders and the Agent…Menezes, F.M. and P.K. Monteiro (2001) “Corruption and Auctions”,working paper, Australian National University.Milgrom, P.M. (1987) “Auction Theory”, Advances in Economic Theory:Fifth World Congres. Cambridge: Cambridge University Press.Murphy, S. P. (1993) “Chelsea Businessman is Said to Allege AttemptedBribery”, Boston Globe, September 22, 1993.Robinson, M.S. (1985), “Collusion and the Choice of Auction”, RandJournal of Economics, 16, 141-145.Yönetim Bilimleri Dergisi (4: 1) 2006 Journal of Administrative Sciences

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