Late and multiple bidding in second price Internet auctions: Theory and evidence concerning different rules for ending an auction

In second price Internet auctions with a fixed end time, such as those on eBay, many bidders submit their bids in the closing minutes or seconds of an auction. We propose an internet auction model, in which very late bids have a positive probability of not being successfully submitted, and show that late bidding in a fixed deadline auction can occur at equilibrium in auctions both with private values and with uncertain, dependent values. Late bidding may also arise out of equilibrium, as a best reply to incremental bidding. However, the strategic advantages of late bidding are severely attenuated in auctions that apply an automatic extension rule such as auctions conducted on Amazon. Field data show that there is more late bidding on eBay than on Amazon, and this difference grows with experience. We also study the incidence of multiple bidding, and its relation to late bidding.     

Profit Maximizing in Auctions of Public Goods

A profit-maximizing auctioneer can provide a public good to a group of agents. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group only if the sum of their bids exceeds a reserve price declared previously by the auctioneer. For the two-bidder case with private values drawn from a uniform distribution we characterize the continuously differentiable symmetric equilibrium bidding functions for the agents, and we find the optimal reserve price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the differentiable bidding functions.     

Endogenous entry and self-selection in private value auctions: An experimental study

This paper presents the results of an experimental study of endogenous entry in first-price independent private value auctions. N potential bidders simultaneously decide whether to participate in an auction or receive a known outside option. In the second stage, entrants submit bids after learning their own private values and the number of entrants. An equilibrium model of heterogeneous risk averse bidders implies a self-selection effect, where bidding in the auction is lower with endogenous entry because only less risk averse bidders enter. This effect is confirmed by the experiment. We also observe excessive entry relative to the theoretical model.     

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.     

Reputation and Perfection in Repeated Common Interest Games

We consider a wide class of repeated common interest games perturbed with one-sided incomplete information: one player (the informed player) might be a commitment type playing the Pareto dominant action. As discounting, which is assumed to be symmetric, and the prior probability of the commitment type go to zero, it is shown that the informed player can be held close to her minmax payoff even when perfection is imposed on the equilibrium.Journal of Economic LiteratureClassification Numbers: C73, D83.     

Empirical Implications of Equilibrium Bidding in First-Price, Symmetric, Common Value Auctions

This paper studies federal auctions for wildcat leases on the Outer Continental Shelf from 1954 to 1970. These are leases where bidders privately acquire (at some cost) noisy, but equally informative, signals about the amount of oil and gas that may be present. We develop tests of rational and equilibrium bidding in a common values model that are implemented using data on bids and ex post values. We also use data on tract location and ex post values to test the comparative static prediction that bidders may bid less aggressively in common value auctions when they expect more competition. We find that bidders are aware of the "winner's curse" and their bidding is largely consistent with equilibrium.     

Researching Preferences,Valuation and Hypothetical Bias

A number of recent papers in environmental economics have focused on the process of researching preferences – agents are uncertain about preferences but with effort may narrow their uncertainty. This issue has arisen in formulating bids in contingent valuation (CV) as well as the debate over the divergence between WTP and WTA. In the context of CV, it has been suggested that the hypothetical nature of the preference elicitation process biases responses. This paper provides both a theoretical model and experimental evidence to contribute to this debate. The model is a model of competitive bidding for a private good with two components that are particularly relevant to the debate. The first component is that bidders are unsure of their own value for the private good but may purchase information about their own value (researching preferences). The second component is that there is a probability that the auction is hypothetical – that the winning bidder will not get the private good and will not pay the winning bid. The experiment tests this theoretical model of bidding equilibrium and analyzes the effects of variations in the parameters (hypotheticalness, information costs and number of agents) on the endogenous variables (such as the proportion of bidders who become informed and the winning bid). Experimental results suggest that an increase in the hypotheticalness of an auction tends to decrease the likelihood that bidders pay for information on their valuation with an ambiguous effect on the winning bid.      

Laboratory Testbeds and Non-Market Valuation: The Case of Bidding Behavior in a Second-Price Auction with an Outside Option

Researchers now use the lab to examine the behavioral underpinnings of valuation before the field application which some argue has less experimental control. But lab valuation work raises its own set of concerns when it uses private goods to explore non-market valuation behavior because private goods have substitutes often unaccounted for in the lab. Therefore, the lab as a tool to testbed field valuation work may be limited. Herein we design an induced valuation experiment to explore bidding behavior in a second-price auction with an outside option that is a perfect substitute for the auction commodity. Theory predicts that rational bidders will consider the prices of outside options when formulating bidding strategies, and will reduce their bids whenever their resale value exceeds the price of the outside option. Our results suggest that bidders account for outside options when formulating bids with behavior following comparative static predictions. In addition, we provide evidence concerning hypothetical versus actual behavior with induced values – the data suggesting a hypothetical bias in the level of bids but not in bid shaving.     

Sealed bid auctions with uncertainty averse bidders

Summary. Traditional analysis of auctions assumes that each bidder's beliefs about opponents' valuations are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox, this paper examines the consequences of relaxing this assumption in the first and second price sealed bid auctions with independent private values. The multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153] is adopted specifically to represent the bidders' (and the auctioneer's) preferences. The unique equilibrium bidding strategy in the first price auction is derived. Moreover, under an interesting parametric specialization of the model, it is shown that the first price auction Pareto dominates the second price auction. Received: December 15, 1995; revised version: February 19, 1997     

Credit contracting and bidding under wealth constraints

Summary. We model credit contracting and bidding in a first-price sealed-bid auction when bidder valuation and wealth are private information. An efficient separating equilibrium exists only if the wealth levels of both bidder types are sufficiently different. If not, high-valuation bidders signal by borrowing more and using less of their wealth – this is inefficient as wealth is a cheaper source of funds. An increase in the amount of borrowing required to signal does not necessarily decrease seller expected revenue. In contrast to separating equilibria, high-valuation bidders adopt pure strategy bids in pooling equilibria. Conditions are identified under which the lower bound on winning bids is higher in pooling than separating equilibria. Received: January 22, 2001; revised version: August 28, 2001     

Bidding for the future: signaling in auctions with an aftermarket

This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.     

Bid rotation and collusion in repeated auctions

This paper studies bidder collusion with communication in repeated auctions when no side transfer is possible. It presents a simple dynamic bid rotation scheme which coordinates bids based on communication history and enables intertemporal transfer of bidders’ payoffs. The paper derives a sufficient condition for such a dynamic scheme to be an equilibrium and characterizes the equilibrium payoffs in a general environment with affiliated signals and private or interdependent values. With IPV, it is shown that this dynamic scheme yields a strictly higher payoff to the bidders than any static collusion scheme which coordinates bids based only on the current reported signals.     

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.     

建筑业招投标中“平均价中标”的实验研究

本文通过实验室实验研究私人独立价值（IPV）假定和共同价值（CV）假定下平均价中标的拍卖。无投标限价时,IPV拍卖的报价迅速收敛至前期平均价,而CV拍卖的报价并未有明显的收敛趋势。有投标限价时,CV拍卖的报价均收敛于投标限价,报价的波动几乎与投标限价的起伏重合,而IPV拍卖的报价却没有随投标限价的起伏而有大幅的波动,仍收敛至前期的平均价格。IPV拍卖的平均报价或中标价格和中标企业的成本没有很大的联系,平均价中标几乎不能配置资源至成本最低的企业。无投标限价CV拍卖虽然避免了“赢家诅咒”问题,但报价普遍偏高;而设立较低的投标限价虽可能降低价格,但和最低价中标拍卖一样,不可避免遭遇“赢家诅咒”问题,同时投标限价很容易成为竞拍者协调报价的共同信息。     

Unraveling in first-price auction

In a private values first-price auction with random number of bidders, the auctioneer has to decide whether to announce or not the actual number of bidders. If the auctioneer cannot commit to any particular announcement policy, then he would like to reveal when the number of bidders is high in order to increase bidding competition. By the same logic, the auctioneer should like to conceal if the number turns out to be small. When bidders' types are independent, full revelation by the auctioneer is shown to be a unique equilibrium with ‘skeptical belief’ as the unique equilibrium belief.     

Symmetric Separating Equilibria in English Auctions

We characterize the set of perfect Bayesian equilibria in symmetric separating strategies in the model of English auctions given by P. R. Milgrom and R. J. Weber (1982, Econometrica50, 1089–1122). There is a continuum of such equilibria. The equilibrium derived by Milgrom and Weber is that in which bids are maximal. Only in the case of pure private values does a restriction to weakly undominated strategies select a unique equilibrium. This has important implications for empirical studies of English auctions, particularly outside the pure private values paradigm. Journal of Economic Literature Classification Numbers: D44, D82.     

Contracting for Infrastructure Projects as Credence Goods

Large infrastructure projects are a major responsibility of urban and regional governments, who usually lack expertise to fully specify the demanded projects. Contractors, typically experts on such projects due to experience with similar projects, advise of the needed design as well as the cost of construction in their bids. Producing the right design is costly. We model such infrastructure projects taking into account their credence goods feature and the costly design effort they require and examine the performance of commonly used contracting methods. We show that when building costs are homogeneous and public information, simultaneous bidding involving shortlisting of two contractors and contingent compensation of both contractors on design efforts outperforms sequential search. If building costs are private information of the contractors and are revealed to them after design cost is sunk, sequential search may be superior to simultaneous bidding.     

Bidding ‘as if’ risk neutral in experimental first price auctions without information feedback

Experimental research on first price sealed bid auctions has usually involved repeated settings with information feedback on winning bids and payoffs after each auction round. Relative to the risk neutral Nash equilibrium, significantly higher bidding has been reported. The present paper reports the results of experimental first price auctions with n=7 where feedback on payoffs and winning bids is withheld. Under these conditions, average bidding is below the risk neutral Nash equilibrium prediction but converges to it with repetition.

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Sealed-bid auctions based on Cobb–Douglas utility function

This paper presents a more general independent private value model based on the assumption that Cobb–Douglas utility function is used to make a tradeoff between the probability of winning the unit and the profit under the first-price and second-price sealed-bid auctions. The equilibrium bidding strategies are given and the seller's expected revenue comparisons are made.     

First-price auction symmetric equilibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the independent private values, first-price auction for any distribution of valuations. The equilibrium strategy is a pure strategy at the continuity points of the distribution and bids a mixed strategy at the discontinuity points of the distribution.