All-pay auction

In economics and game theory, an all-pay auction is an auction in which every bidder must pay regardless of whether they win the prize, which is awarded to the highest bidder as in a conventional auction.

In an all-pay auction, the Nash equilibrium is such that each bidder plays a mixed strategy and their expected pay-off is zero. ^[1] The seller's expected revenue is equal to the value of the prize. However, some experiments have shown that over-bidding is common. That is, the seller's revenue frequently exceeds that of the value of the prize, and in repeated games even bidders that win the prize frequently will most likely make a loss in the long run.^[2]

Forms of all-pay auctions

The most straightforward form of an all-pay auction is a Tullock auction, sometimes called a Tullock lottery, in which everyone submits a bid but both the losers and the winners pay their submitted bids. This is instrumental in describing certain ideas in public choice economics. The dollar auction is a two player Tullock auction, or a multiplayer game in which only the two highest bidders pay their bids.

A conventional lottery or raffle can also be seen as a related process, since all ticket-holders have paid but only one gets the prize. Commonplace practical examples of all-pay auctions can be found on several "penny auction"/bidding fee auction websites.

Other forms of all-pay auctions exist, such as a war of attrition (also known as biological auctions^[3]), in which the highest bidder wins, but all (or more typically, both) bidders pay only the lower bid. The war of attrition is used by biologists to model conventional contests, or agonistic interactions resolved without recourse to physical aggression.

References

↑ Jehiel P, Moldovanu B (2006) Allocative and informational externalities in auctions and related mechanisms. In: Blundell R, Newey WK, Persson T (eds) Advances in Economics and Econometrics: Volume 1: Theory and Applications, Ninth World Congress, vol 1, Cambridge University Press, chap 3
↑ Gneezy and Smorodinsky (2006), All-pay auctions - An experimental study, Journal of Economic Behavior & Organization, Vol 61, pp. 255–275
↑ Chatterjee, Reiter, and Nowak (2012), Evolutionary Dynamics of Biological Auctions, Theoretical Population Biology, Vol 81, pp. 69–80

External links

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Screening game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game Potential game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Thomas Schelling William Vickrey

See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons Tyranny of small decisions

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