Wars of Attrition with Stochastic Competition
We extend the all-pay auctions analysis of Krishna and Morgan (1997) to a stochastic competition setting. In the war of attrition it does not directly follow from the first order condition that the bidding equilibrium strategy is a weighted average of the bidding equilibrium strategies that would be chosen for each number of bidders. This result contrasts with the characterization of the bidding equilibrium strategies in the first-price all-pay auction as well as the winner-pay auctions. Our findings are applicable to future works on contests and charity auctions.
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