Equilibrium existence and expected payoffs in all-pay auctions with constraints
研究了玩家策略受上限约束的全支付拍卖，证明了均衡存在性，并给出了玩家期望收益的简单公式，可直接用于政策分析等应用，无需推导完整均衡。
Abstract This paper introduces constraints on player choices in a broad class of all-pay auctions by allowing for upper bounds on players’ strategy sets. It proves the existence of equilibrium and derives simple closed-form formulae for players’ expected payoffs in any equilibrium. These formulae are straightforward to calculate in applications and do not require the derivation of the equilibrium or equilibria. This may be useful because: (i) In some applications players’ expected payoffs are the main item of interest. For example, one may be concerned about the effect of a policy on the market participants. In these cases the results can be used directly, bypassing the need for the full derivation of the equilibrium. (ii) In all-pay auctions, equilibrium is typically in mixed strategies. So in applications where the full characterization of the equilibrium is of interest, finding the players’ expected payoffs is a crucial first step in the derivation of the equilibrium.