In a standard all-pay auction, every player pays its bid or effort cost, and the highest bid receives the prize. With a value , unit effort cost, and winning probability , player has quasilinear utility . Equal highest bids require an explicit tie rule.
For effective prizes and unit effort costs, equilibrium effort CDFs on are and . The weaker player has an atom at zero. Incremental utilities are and zero, and winning probabilities are and . Direct payoff indifference and exclusion of larger bids verify the Nash equilibrium. A further player with effective prize at most cannot profit by entering against these distributions.
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An all-pay auction is a type of auction in which all participants must pay their bids regardless of whether they win the auction or not. Unlike traditional auctions where only the highest bidder pays their bid amount, in an all-pay auction, every bidder pays what they bid, and the item is awarded to the highest bidder. This type of auction can create unique strategic considerations for bidders, as all participants have to commit their resources upfront.