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.  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.
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), 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.
- 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
- Econ Talk podcast where economic professors discuss grants as an all-pay or Tullock auction.
- What do we know about penny auctions? - Toomas Hinnosaar
- Penny Auctions - Toomas Hinnosaar
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