Equilibrium existence and expected payoffs in all-pay auctions with constraints (Q6107386)

In this article, the authors incorporate constraints on players' actions in a broad class of complete information all-pay auctions by imposing upper bounds on the strategy sets of some, all or none of the players. It is shown that equilibrium exists. More precisely, the authors derive simple closed form formulae for players' equilibrium expected payoffs. The results are useful for two reasons: (i) In some applications player's expected payoffs are the main item of interest; (ii) In all-pay auctions, equilibrium is typically in mixed strategies. Section 2 presents the model. Section 5 provides an illustrative application taken from the literature showing how the results can be used in practice.