Internet auctions with many traders

We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogeneous good, set reserve prices at their own second-price auctions. Each buyer has private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between auctions. We characterize a perfect Bayesian equilibrium for this decentralized dynamic mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform price. In a large but finite market, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex post efficiency is achieved. Buyers’ strategies in this equilibrium are simple and do not depend on their beliefs about other buyers’ valuations, or the number of buyers and sellers.     

A short proof of the Bulow-Klemperer auctions vs. negotiations result

Summary. Bulow and Klemperer [1] have provided an upper bound on the value of bargaining power for a seller of an indivisible object. Specifically, negotiating optimally with N buyers yields lower revenue than an English auction with N + 1 buyers. In this paper, a short and intuitive proof of this result is presented.Received: 2 August 2004, Revised: 6 December 2004, JEL Classification Numbers: C78, D44, D82.I would like to thank Per B. Overgaard and an anonymous referee for many valuable comments.     

Auctions with cross-shareholdings

Summary. We study the effect of cross-shareholding among two competing firms on their bidding behavior and the expected sales revenue for the seller in an auction environment. The bidders private signals are independent, and the model encompasses the private values model and a particular common value model as special cases. When cross-shareholding is symmetric, the bids decrease towards the collusive level as the degree of cross-shareholding increases. The Revenue Equivalence result no longer holds: the first-price auction generates higher expected revenue for the seller than the second-price auction.With asymmetric cross-shareholding, revenue comparisons are only possible in the common value setting. Expected revenue for the seller is again higher in the first-price than in the second price auction. Bidding behavior in the second-price auction is more sensitive to changes in cross-shareholding and the value environment than in the first-price auction.Received: 18 September 2000, Revised: 27 May 2003, JEL Classification Numbers: C72, D44.Correspondence to: Sudipto DasguptaWe thank Sugato Bhattacharyya, Paul Klemperer, Kunal Sengupta and Guofu Tan for helpful discussions, and an anonymous referee for suggestions that improved the paper. The usual disclaimer, of course, applies.     

Collusion in one-shot second-price auctions

Summary. Most of the literature on collusive behavior in auctions ignores two important issues that make collusion difficult to sustain at least in one-shot interactions: the detection of cheating and the verification of bids. Colluding bidders may deceive each other by using shill bidders. Also, if the identities of the bidders and their bids are not published then it would be difficult to verify the bid of a colluding bidder. This paper addresses these problems in one shot second price auctions where one bidder offers another bidder a side payment in exchange for not participating in the auction, while the number of other bidders is stochastic. In spite of the barriers to collusion mentioned above, a simple side payment mechanism which depends only on the auction price is introduced. It induces a successful collusion, eliminates the verification problem, provides no incentive for the use of shill bidders and guarantees that the proponent obtains ex-post non-negative payoff. The colluding bidders are ex-ante strictly better off compared with the competitive case, irrespective of their types.Received: 27 November 2002, Revised: 28 January 2005, JEL Classification Numbers: C72, D44, D82.Yair Tauman: Correspondence toWe would like to thank an anonymous referee for very valuable comments and suggestions that significantly improved the paper. We thank Shmuel Zamir for a helpful discussion.     

Finding and retaining the dominant strategy: The second-price, English and ‘sealed offer’ English auctions

Using experiments in a procurement setting, this study examined the performance abilities of three auctions: the second-price, English, and a new ‘sealed offer’ English. Additionally, to see if dominant strategy learning would be transferred, after fifteen periods with one of the three auctions, all subjects completed a second 15 periods with the second-price auction. The English auction performed best overall. However, only limited learning was found to occur, with some subjects that had adopted the dominant strategy in the English switching in the second-price. Lessons from the new mechanism transferred better, but initial learning of the dominant strategy was slower.     

Mental processes and strategic equilibration: An fMRI study of selling strategies in second price auctions

This study is the first to attempt to isolate a relationship between cognitive activity and equilibration to a Nash Equilibrium. Subjects, while undergoing fMRI scans of brain activity, participated in second price auctions against a single competitor following predetermined strategy that was unknown to the subject. For this auction there is a unique strategy that will maximize the subjects’ earnings, which is also a Nash equilibrium of the associated game theoretic model of the auction. As is the case with all games, the bidding strategies of subjects participating in second price auctions most often do not reflect the equilibrium bidding strategy at first but with experience, typically exhibit a process of equilibration, or convergence toward the equilibrium. This research is focused on the process of convergence.In the data reported here subjects participated in sixteen auctions, after which all subjects were told the strategy that will maximize their revenues, the theoretical equilibrium. Following that announcement, sixteen more auctions were performed. The question posed by the research concerns the mental activity that might accompany equilibration as it is observed in the bidding behavior. Does brain activation differ between being equilibrated and non-equilibrated in the sense of a bidding strategy? If so, are their differences in the location of activation during and after equilibration? We found significant activation in the frontal pole especially in Brodmann’s area 10, the anterior cingulate cortex, the amygdala and the basal forebrain. There was significantly more activation in the basal forebrain and the anterior cingulate cortex during the first sixteen auctions than in the second sixteen. The activity in the amygdala shifted from the right side to the left after the solution was given.     

When and why not to auction

Summary. Standard auctions are known to be a revenue-maximizing way to sell an object under broad conditions when buyers are symmetric and have independent private valuations. We show that when buyers have interdependent valuations, auctions may lose their advantage, even if symmetry and independence of information are maintained. In particular, simple alternative selling mechanisms that sometimes allow a buyer who does not have the highest valuation to win the object will in general increase all buyers willingness to pay, possibly enough to offset the loss to the seller of not always selling to the buyer with the greatest willingness to pay.Received: 18 June 2003, Revised: 7 September 2004, JEL Classification Numbers: D44, D82. Correspondence to: Colin M. CampbellWe thank Richard McLean, Dan Kovenock, two referees, and seminar participants at the University of Pittsburgh, Johns Hopkins University, Washington University, the Federal Communications Commission, the Institute for Advanced Studies at Princeton, UC-Santa Barbara, UC-Santa Cruz, and the Ohio State University Department of Finance for helpful suggestions. We thank the NSF for funding.     

The sale of small firms: a multidimensional analysis

Summary. This paper endogeneizes the security voting structure in an auction mechanism used to sell a small firm. The design of security voting structure allows the seller to choose between two objectives which are not mutually consistent. If the seller wants to maximize his revenue, he should retain some shares to benefit from the future dividends generated by the acquirer. At the opposite, if he wants to sell his firm to the most efficient candidate, he should sell all the shares. Received: July 4, 2001; revised version: October 31, 2002 RID="*" ID="*" The paper has benefited from a number of comments from the anonymous referees. Correspondence to: C. At     

Auctions of licences and market structure

Summary. This paper studies sequential auctions of licences to participate in a symmetric market game. Assuming that the rate at which industry profits decrease with repeated entry is not too large, at the unique solution either a single firm preempts entry altogether or entry occurs in every stage, depending on the net benefit of complete preemption to an incumbent. If we relax the assumption, a third outcome can occur: two firms may coordinate their choices to avoid further entry. The analysis employs a new refinement of Nash equilibrium, the concept of recursively undominated equilibrium. Received: February 25, 2000; revised version: September 12, 2000     

Time is money: The effect of clock speed on seller’s revenue in Dutch auctions

We study the role of timing in auctions under the premise that time is a valuable resource. When one object is for sale, Dutch and first-price sealed bid auctions are strategically equivalent in standard models, and therefore, they should yield the same revenue for the auctioneer. We study Dutch and first-price sealed bid auctions in the laboratory, with a specific emphasis on the speed of the clock in the Dutch auction. At fast clock speeds, revenue in the Dutch auction is significantly lower than it is in the sealed bid auction. When the clock is sufficiently slow, however, revenue in the Dutch auction is higher than the revenue in the sealed bid auction. We develop and test a simple model of auctions with impatient bidders that is consistent with these laboratory findings.

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A simple model of coalitional bidding

Summary. We analyze a model of coalitional bidding in which coalitions form endogenously and compete with each other. Since the nature of this competition influences the way in which agents organize themselves into coalitions, our main aim is to characterize the equilibrium coalition structure and the resulting bids. We do so in a simple model in which the seller may have good reason to allow joint bidding. In particular, we study a model in which the agents are budget constrained, and are allowed to form coalitions to pool their finances before engaging in the first price auction. We show that if the budget constraint is very severe, the equilibrium coalition structure consists of two coalitions, one slightly larger than the other; interestingly, it is not the grand coalition. This equilibrium coalition structure is one which yields (approximately) the maximum expected revenue. Thus the seller can induce the optimal (revenue maximizing) degree of cooperation among budget constrained buyers simply by permitting them to collude. Received: June 25, 1999; revised version: November 13, 2000     

Framing the first-price auction

We revisit the result that, in laboratory independent private values auction, the first-price sealed bid and descending clock (or Dutch) implementations are not isomorphic. We investigate the hypothesis that this arises from framing and presentation effects. Our design focuses on a careful construction of subject interfaces that present the two environments as similarly as possible. Our sessions also consist of more auction periods to test whether any initial framing effects subsequently decrease over time. We find the difference between the implementations persists. To further investigate the difference, we report on an intermediate implementation which operates like the Dutch auction, but in which the clock continues to tick to the lowest price without informing bidders when others have bid on the object. JEL Classification D44, C90 Deceased     

Ratifiability of efficient collusive mechanisms in second-price auctions with participation costs

We investigate whether efficient collusive bidding mechanisms are affected by potential information leakage from bidders' decisions to participate in them within the independent private values setting. We apply the concept of ratifiability introduced by Cramton and Palfrey [Cramton, P.C., Palfrey, T.R., 1995, Ratifiable mechanisms: Learning from disagreement, Games Econ. Behav. 10 (2), 255–283] and show that when the seller uses a second-price auction with participation costs, the standard efficient cartel mechanisms such as pre-auction knockouts analyzed in the literature will not be ratified by cartel members. A high-value bidder benefits from vetoing the cartel mechanism since doing so sends a credible signal that she has high value, which in turn discourages other bidders from participating in the seller's auction.     

Dissolving a partnership (un)fairly

Summary. In an incomplete information, common values setting with risk-neutral agents, we consider mechanisms for allocating the assets of a dissolving partnership where the mechanism designer has no information about the distribution of signals of the agents. We find that the divide and choose mechanism systematically favors the chooser and hence fails on the grounds of fairness. We also examine the fairness properties of the winning and losing bid auctions and show that they systematically favor winning (resp. losing) bidder in ex post allocation of surplus. Finally, we show that a binding arbitration mechanism implements fair allocations.Received: 17 May 2002, Revised: 5 June 2003, JEL Classification Numbers: D39, D44I thank an anonymous referee for extremely helpful suggestions. I also gratefully acknowledge the support of the National Science Foundation and the Hoover Institution.     

Revealing information in auctions: the allocation effect

When there are two bidders, releasing independent information in an English auction with private values makes the seller worse off. However, this is no longer true with more bidders: when there is enough competition, revelation benefits the auctioneer. In three examples the dividing case is shown to be three bidders. This allocation effect applies to other standard auctions and parallels the bundling decision in a multi-unit auction. I would like to thank Jeremy Bulow, Willie Fuchs, Paul Klemperer, Rob McMillan, Phil Reny, Jeff Zwiebel and especially Andy Skrzypacz. I also grateful to two referees and an Associate Editor for a number of helpful comments.     

Are bidders in auctions anchored by their bidder number?

This article examines whether bidders in a school fundraising auction were anchored by their bidder number. We find no evidence that they were.     

Vickrey auctions with reserve pricing

Summary. We generalize the Vickrey auction to allow for reserve pricing in a multi-unit auction with interdependent values. In the Vickrey auction with reserve pricing, the seller determines the quantity to be made available as a function of the bidders' reports of private information, and then efficiently allocates this quantity among the bidders. Truthful bidding is a dominant strategy with private values and an ex post equilibrium with interdependent values. If the auction is followed by resale, then truthful bidding remains an equilibrium in the auction-plus-resale game. In settings with perfect resale, the Vickrey auction with reserve pricing maximizes seller revenues.Received: 31 December 2002, Revised: 5 May 2003, JEL Classification Numbers: D44, C78, D82.Correspondence to: Lawrence M. AusubelThe authors gratefully acknowledge the generous support of National Science Foundation Grants SES-97-31025, SES-01-12906 and IIS-02-05489. We appreciate valuable comments from Ilya Segal. Special thanks go to Mordecai Kurz, who served as Larry's dissertation advisor and who introduced both authors to the economics profession back at IMSSS at Stanford. Congratulations and best wishes are extended to Mordecai and his family on the happy occasion of the publication of Assets, Beliefs, and Equilibria in Economic Dynamics: Essays in Honor of Mordecai Kurz, in which this article also appears.