Information acquisition during a descending auction

We compare the effects of information acquisition during a descending auction with its static counterpart, the first-price sealed-bid auction. In a framework with heterogeneous prior information, we show that an equilibrium with information acquisition exists in both auction formats. We show that everything else equal information acquisition is more desirable in the dynamic auction. Moreover, we characterize a set of parameter values where more information is acquired in the dynamic auction in equilibrium. If the costs of information acquisition are sufficiently low, the sealed-bid auction generates more revenue although the descending auction is more efficient.     

Non-monotoniticies and the all-pay auction tie-breaking rule

Discontinuous games, such as auctions, may require special tie-breaking rules to guarantee equilibrium existence. The best results available ensure equilibrium existence only in mixed strategy with endogenously defined tie-breaking rules and communication of private information. We show that an all-pay auction tie-breaking rule is sufficient for the existence of pure strategy equilibrium in a class of auctions. The rule is explicitly defined and does not require communication of private information. We also characterize when special tie-breaking rules are really needed.      

Best-of-three all-pay auctions

We study a best-of-three all-pay auction. It is shown that with values of winning and without values of losing, this auction is less productive (the players’ total expected effort is smaller) than the one-stage all-pay auction. However, with different values of losing over the contest’s stages it may be more productive than the one-stage all-pay auction.     

On the continuous equilibria of affiliated-value,all-pay auctions with private budget constraints

We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endowments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two auction formats is generally not possible. Equilibria with discontinuous bidding strategies are discussed.     

The best-shot all-pay (group) auction with complete information

We analyze an all-pay group contest in which individual members’ efforts are aggregated via the best-shot technology and the prize is a public good for the winning group. The interplay of within-group free-riding and across-group competition allows for a wide variety of equilibria, according to how well groups overcome internal free-riding. In contrast with the existing literature, we derive equilibria of a symmetric model in which multiple agents per group are active. Our findings differ qualitatively from those of the individualistic all-pay auction: rents are not necessarily dissipated in equilibrium, total expected efforts vary across equilibria, and participation is expected to be greater. Moreover, equilibria with greater symmetry of behavior within a group are shown to have more “wasted” effort but also greater payoffs as overall efforts are lower. In contrast to standard economic intuition, free-riding can be beneficial for players as it reduces competition among groups. Examples of asymmetric group contests are also studied.     

Sequential two-prize contests

We study a two-stage all-pay auction with two identical prizes. In each stage, the players compete for one prize. Each player may win either one or two prizes. We analyze the unique subgame-perfect equilibrium of our model with two players where each player??s marginal values for the prizes are decreasing, constant, or increasing. We also analyze an equilibrium of the model with more than two players where each player??s marginal values for the prizes are nonincreasing.     

Lottery versus all-pay auction contests: A revenue dominance theorem

We allow a contest organizer to bias a contest in a discriminatory way; i.e., she can favor specific contestants by designing the contest rule in order to maximize total equilibrium effort (resp. revenue). The two predominant contest regimes are considered, all-pay auctions and lottery contests. For all-pay auctions the optimal bias is derived in closed form: It implies extreme competitive pressure among active contestants and low endogenous participation rates. Moreover, the exclusion principle advanced by Baye et al. (1993) becomes obsolete in this case. In contrast, the optimally biased lottery induces a higher number of actively participating contestants due to softer competition. Our main result regarding total revenue comparison under the optimal biases reveals that the all-pay auction revenue-dominates the lottery contest for all levels of heterogeneity among contestants. The incentive effect due to a strongly discriminating contest rule (all-pay auction) dominates the participation effect due to a weakly discriminating contest rule (lottery).     

Unfair contests

Real-world contests are often “unfair” in the sense that outperforming all rivals may not be enough to be the winner, because some contestants are favored by the allocation rule, while others are handicapped. This paper analyzes an unfair, two-player discriminatory contest (all-pay auction) with private values. We characterize equilibrium strategies, provide closed form solutions, and illustrate additional strategic issues arising in such unfair contests.     

Difference-Form Contests and the Robustness of All-Pay Auctions

In much of the existing literature on rent-seeking games, the outcome of the contest is either infinitely sensitive or relatively insensitive to contestants' efforts. The current paper presents a family of contest games that permit characterization of equilibrium for all levels of sensitivity of the outcome to contestants' efforts. Specifically, the outcome of the contest depends on the difference between efforts, which encompass the lottery and the all-pay auction as polar cases. The equilibrium converges to that of the all-pay auction as the probability of winning the prize grows infinitely sensitive to one's effort, and the main qualitative features of equilibrium persist over a large parameter region. Journal of Economic Literature Classification Numbers: D44, D72.     

Maximum efforts in contests with asymmetric valuations

Efforts may be reduced when players with different valuations participate in a contest. This paper considers the problem of designing a contest to elicit maximum aggregate effort from players with asymmetric valuations. Optimal designs for different classes of contest technologies are computed and characterized. A value weighted contest is optimal in the concave case. In the unconstrained case, the optimal contest is equivalent to a first price all-pay auction with a reserve price. The optimal design discounts the effort of the high valuation player in order to induce him to compete vigorously.     

The all-pay auction with complete information

Summary In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium.We are grateful to Jacques Crémer, Chuangyin Dang, Jürgen Dennert, Chaim Fershtman, Martin Hellwig, Arthur Robson, Heinrich Ursprung, Eric van Damme, Ton Vorst, and the referees for helpful comments. We benefitted from presentations at the World Congress of the Econometric Society in Barcelona, the European Meeting on the Economics of Information at Tilburg University, the Midwest Mathematical Economics Meetings at the University of Illinois, and seminars at Texas A&M University, The Pennsylvania State University, Tilburg University and the University of Montreal. Baye is grateful for support from the CentER for Economic Research at Tilburg University and the Tinbergen Institute where earlier versions of this paper were completed. Kovenock acknowledges support from Erasmus Universiteit Rotterdam, the Tinbergen Institute, the Center for Economic Studies at the University of Munich, the Institut d'Analisi Economica CSIC at the Universitat Autonoma de Barcelona, the Krannert School of Management, and the Jay N. Ross Young Faculty Scholar Award.     

Banning Bidders from All-pay Auctions

We consider an all-pay auction with complete information among the bidders; the seller does not observe the bidders’ values. We show that for some information structures in which the seller has a small uncertainty about the valuations, it is profitable for him to exclude from the auction all but two (randomly selected) bidders even though the latter are ex ante identical from his point of view.I am grateful to Paolo Bertoletti who introduced me to this topic and provided useful comments. I also thank Dan Kovenock (Co-Editor) and two anonymous referees for suggestions which considerably improved the exposition.     

The value of information in asymmetric all-pay auctions

This note analyzes a two-player all-pay auction with incomplete information. More precisely, one bidder is uncertain about the size of the initial advantage of his rival modeled as a head start in the auction.I derive the unique Bayesian Nash equilibrium outcome for a large class of cumulative distribution functions of the head start. The stronger player generates an informational rent if and only if his head start distribution is not stochastically dominated by a uniform distribution. I identify why my results for an uncertain head start differ qualitatively from uncertainty about a cost function or a valuation.     

The symmetric multiple prize all-pay auction with complete information

This paper extends the analysis of the n-player all-pay auction with complete information to cover the case of m≤n prizes, valued in weakly decreasing order, but symmetrically across players. We provide a complete characterization of the Nash equilibrium distributions for this class of auctions and provide an exact expression for the expected revenue generated.     

Charitable asymmetric bidders

Recent papers show that the all‐pay auction is better at raising money for charity than the first‐price auction with symmetric bidders under incomplete information. Yet, this result is lost with sufficiently asymmetric bidders under complete information. In this paper, we consider a framework on charity auctions with asymmetric bidders under some incomplete information. We find that the all‐pay auction still raises more money than the first‐price auction. Thus, the all‐pay auction should be seriously considered when one wants to organize a charity auction.     

Asymmetric Nash equilibrium in emission rights auctions

This paper studies the problems of emission rights auctions, and presents a uniform price auction mechanism based on three assumptions, i.e., all buyers are asymmetric, every buyer submits a nonincreasing continuous demand function, and every buyer's valuation to per unit of the emission rights is common value information. It focuses on solving the asymmetric Nash equilibrium for this auction mechanism. It concludes that there exist multiple Nash equilibria in our auction mechanism, but the arbitrary low equilibrium prices cannot emerge. We also give several suggestions on how to induce the auction to a desired ideal equilibrium state in mechanism design of emission rights auctions.     

Expected revenue of all-pay and first-price sealed-bid auctions with affiliated signals

In the general symmetric auction framework of Milgrom and Weber (1982) it is shown—as a new manifestation of thelinkage principle—that the all-pay sealed-bid auction yieldshigher expected revenue than the standard first-price sealed-bid auction. This raises the question why sealed-bid auctions of the standard first-price variety are observed in practice whereas the all-pay variety is not.     

Optimal auctions with information acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.     

Investment coordination in network industries: the case of electricity grid and electricity generation

Liberalization of network industries frequently separates the network from the other parts of the industry. This is important in particular for the electricity industry where private firms invest into generation facilities, while network investments usually are controlled by regulators. We discuss two regulatory regimes. First, the regulator can only decide on the network extension. Second, she can additionally use a “capacity market” with payments contingent on private generation investment. For the first case, we find that even absent asymmetric information, a lack of regulatory commitment can cause inefficiently high or inefficiently low investments. For the second case, we develop a standard handicap auction which implements the first best under asymmetric information if there are no shadow costs of public funds. With shadow costs, no simple mechanism can implement the second best outcome.     

Rent seeking and rent dissipation: A neutrality result

We consider rent seeking contests between at least two agents who might value the prize differently. We capture a wide range of institutional aspects of contests by analyzing a class of contest success functions fulfilling several properties. The main properties are anonymity and a condition on the elasticity of a rent seeker's win probability with respect to her effort. We show the existence of a mixed-strategy equilibrium and establish equilibrium payoffs. In this equilibrium complete rent dissipation holds. Our results imply a partial robustness result for the all-pay auction.