All-pay auction
Encyclopedia
In economics
and game theory
an all-pay auction, is an auction
in which all bidders must pay regardless of whether they win the prize, which is awarded to the highest bidder as in a conventional auction. The all-pay auction is often used to model lobbying
(bids are political contributions), or other competitions such as contests between animals.
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.
Other forms of all-pay auctions exist, such as the war of attrition
, in which the highest bidder wins, but all (or both, more typically) 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.
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.
Commonplace practical examples of all-pay auctions can be found on several bidding fee auction
websites.
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
an all-pay auction, is an auction
Auction
An auction is a process of buying and selling goods or services by offering them up for bid, taking bids, and then selling the item to the highest bidder...
in which all bidders must pay regardless of whether they win the prize, which is awarded to the highest bidder as in a conventional auction. The all-pay auction is often used to model lobbying
Lobbying
Lobbying is the act of attempting to influence decisions made by officials in the government, most often legislators or members of regulatory agencies. Lobbying is done by various people or groups, from private-sector individuals or corporations, fellow legislators or government officials, or...
(bids are political contributions), or other competitions such as contests between animals.
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
Dollar auction
The dollar auction is a non-zero sum sequential game designed by economist Martin Shubik to illustrate a paradox brought about by traditional rational choice theory in which players with perfect information in the game are compelled to make an ultimately irrational decision based completely on a...
is a two player Tullock auction, or a multiplayer game in which only the two highest bidders pay their bids.
A conventional lottery
Lottery
A lottery is a form of gambling which involves the drawing of lots for a prize.Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments...
or raffle
Raffle
A raffle is a competition in which people obtain numbered tickets, each ticket having the chance of winning a prize. At a set time, the winners are drawn from a container holding a copy of every number...
can also be seen as a related process, since all ticket-holders have paid but only one gets the prize.
Other forms of all-pay auctions exist, such as the war of attrition
War of attrition (game)
In game theory, the war of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while constantly accumulating costs over the time t that the contest lasts. The model was originally formulated by John Maynard Smith, a mixed evolutionary stable...
, in which the highest bidder wins, but all (or both, more typically) bidders pay only the lower bid. The war of attrition is used by biologists to model conventional contests, or agonistic interactions
Agonistic behaviour
In ethology, agonistic behaviour is any social behaviour related to fighting. Thus it is broader than aggressive behaviour because it includes not only actual aggression but also threats, displays, retreats, placating aggressors, and conciliation. The term was coined by Scott and Fredericson in 1951...
resolved without recourse to physical aggression.
In an all-pay auction the Nash Equilibrium
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
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
Experimental economics
Experimental economics is the application of experimental methods to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in...
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.
Commonplace practical examples of all-pay auctions can be found on several bidding fee auction
Bidding fee auction
A bidding fee auction, also called a penny auction, is a type of all-pay auction in which participants must pay a non-refundable fee to place a small incremental bid. When time expires, the last participant to have placed a bid wins the item and also pays the final bid price, which is purportedly...
websites.