Unobserved correlation in private-value ascending auctions

In private-value ascending auctions, the winner's willingness to pay is not observed, leading to underidentification of many econometric models. I calculate tight bounds on expected revenue and optimal reserve price for the case of symmetric and affiliated private values.     

Asymmetric common-value auctions with applications to private-value auctions with resale

We study a model of common-value auctions with two bidders in which bidders’ private information are independently and asymmetrically distributed. We present sufficient and necessary conditions, respectively, under which the expected revenues from first-price and second-price auctions can be ranked. Using these conditions and a bid-equivalence between common-value auctions and private-value auctions with resale, we extend the revenue-ranking result of Hafalir and Krishna [Am Econ Rev 98, 2008a] and provide necessary conditions for their ranking to hold. In addition, we provide sufficient and necessary conditions for the opposite ranking of revenues, respectively. Our analysis helps clarify the roles of two forms of regularity assumptions (buyer-regularity and seller-regularity) in ranking revenues and illustrates how revenue ranking is linked to submodularity and supermodularity of the common-value function and to a single-crossing property of a function derived from the monopoly or monopsony pricing function in the resale stage.     

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.     

Multi-unit demand auctions with synergies: behavior in sealed-bid versus ascending-bid uniform-price auctions

We construct a relatively simple model of bidding with synergies and solve it for both open outcry and sealed-bid uniform-price auctions. The essential behavioral forces involved in these auctions are: (1) A demand reduction force resulting from the monopsony power that bidders with multiple-unit demands have when synergies are relatively inconsequential, and (2) Bidding above stand-alone values in order to capture significant complementarities between units. The latter creates a potential “exposure problem,” as bidders may win only parts of a package and earn negative profits. Bidding outcomes are closer to equilibrium in clock compared to sealed-bid auctions. However, there are substantial and systematic deviations from equilibrium, with patterns of out-of-equilibrium play differing systematically between the two auction formats. These patterns of out-of-equilibrium play are analyzed, along with their effects on revenue and efficiency.     

Information revelation in auctions

Auction theory has emphasized the importance of private information to the profits of bidders. However, the theory has failed to consider to what extent initially private information will remain private. We show that in a variety of contexts bidders will reveal their information, even if this information revelation is (ex ante) detrimental to them. Similarly, a seller may reveal her information although this revelation lowers revenues. We also show that bidders may be harmed by private information, even in contexts where more information has traditionally been presumed to be beneficial.     

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.     

Simultaneous use of auctions and posted prices

I consider a model in which several identical objects are sold simultaneously via an auction and a posted price mechanism. The model explains several empirical regularities regarding bidding behavior in eBay auctions such as the finding that some bidders bid multiple times over the course of the auction, and that bidders tend to bid with greater frequency near the end of the auction than the beginning. I also show that sellers prefer to simultaneously use auctions and posted prices than to use either mechanism individually.     

Nonstandard bidder behavior in real-world auctions

Empirical work on auctions has found that bidders deviate from standard behavior in important ways. We investigate a range of these behaviors, including nonrational herding, auction fever, quasi-endowment effect, and escalation of commitment. Our innovations are to more completely control for unobservables by using new data from a field experiment on eBay, and by accounting for censoring of bids below the starting price. Consistent with standard auction theory and in contrast to the predictions of the nonstandard behaviors, we find that auction starting price has no effect on bidder willingness to pay in a private-values setting. We conclude that there is little evidence that these nonstandard behaviors are important in the field.     

Auction fever: Rising revenue in second-price auction formats

The prevalent term “auction fever” visualizes that ascending auctions – inconsistent with theory – are likely to provoke higher bids than one-shot auctions. To explore and isolate causes of auction fever experimentally, we design four different strategy-proof auction formats and order these according to expected rising bids based on pseudo-endowment effect arguments (psychological ownership and disparity between willingness to pay and willingness to accept). Observed revenues in the experiment in the four formats rank as expected if bidders have private uncertain values (the private information of a bidder is the distribution of her value). A control treatment supports our view that the traditional private certain values approach prevents auction fever in the laboratory. Another control treatment with a procurement auction relates the auction fever bids to bids in a one-shot auction with real endowments. We conclude that, when bidders are uncertain about their valuations, auctions that foster pseudo-endowment may raise bids and revenues.     

Biased procurement auctions

In a complex procurement a buyer may consider biasing the auction rules in order to account for differences in product characteristics offered by the sellers. This paper studies the gathering, disclosure and use of information about this bias. While we also describe the optimal procurement auction in our setting, the main focus of the paper is on the case where the buyer does not have commitment power. We find that without commitment full disclosure of the buyer’s preferences is optimal. Furthermore, lack of commitment distorts the buyer’s incentives to learn about its preferences: unlike the commitment case, without commitment the value of this information can be negative. Based on Chapter 3 of my Ph.D. dissertation at Stanford University. I gratefully acknowledge the support of a John M. Olin Dissertation Fellowship and a Melvin and Joan Lane Stanford Graduate Fellowship. Thanks to Pat Bajari, Tim Bresnahan, Vinicius Carrasco, George Deltas, Jonathan Levin, Paul Milgrom, Ilya Segal and an anonymous referee for valuable suggestions.     

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.     

Equilibrium selection in common-value second-price auctions

This note considers equilibrium selection in common-value second-price auctions with two bidders. We show that for each ex post equilibrium in continuous and undominated strategies, a sequence of “almost common-value” auctions can be constructed such that each of them possesses a unique undominated and continuous equilibrium and the corresponding sequence of equilibria converges to that ex post equilibrium. As an implication, no equilibrium selection of this model based on perturbations seems to be more convincing than others.     

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.     

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.     

Private monitoring in auctions

We study infinitely repeated first-price auctions in which a bidder only learns whether or not he won the object. While repetition of the stage-game equilibrium is the unique Nash equilibrium in public strategies, with patient bidders there are simple Nash equilibria in private strategies that improve on bid rotation. Sequential rationality is appropriately captured by essentially perfect Bayesian equilibrium (EPBE), which ignores behavior after irrelevant histories. Our main result is the construction of EPBEa that improve upon bid rotation. Assuming symmetry, the exclusionary schemes of Skrzypacz and Hopenhayn [Tacit collusion in repeated auctions, J. Econ. Theory 114 (2004), 153–169], including asymptotically efficient ones, are supported as EPBEa.     

Computationally-feasible truthful auctions for convex bundles

In many economic settings, like spectrum and real-estate auctions, geometric figures on the plane are for sale. Each bidder bids for his desired figure, and the auctioneer has to choose a set of disjoint figures that maximizes the social welfare. In this work, we design mechanisms that are both incentive compatible and computationally feasible for these environments. Since the underlying algorithmic problem is computationally hard, these mechanisms cannot always achieve the optimal welfare; Nevertheless, they do guarantee a fraction of the optimal solution. We differentiate between two information models—when both the desired figures and their values are unknown to the auctioneer or when only the agents' values are private data. We guarantee different fractions of the optimal welfare for each information model and for different families of figures (e.g., arbitrary convex figures or axis-aligned rectangles). We suggest using a measure on the geometric diversity of the figures for expressing the quality of the approximations that our mechanisms provide.     

投标与拍卖的决策理论方法

本文介绍国内很少涉及的国际投标和拍卖中的一些重要概念和基本问题，重点综述国际投标与拍卖的决策理论模型与方法的发展历史与现状。     

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.