We study discrete two player all-pay auction with complete information. We provide full characterization of mixed strategy Nash equilibria and show that they constitute a subset of Nash equilibria of discrete General Lotto game. We show that equilibria are not unique in general but they are interchangeable. We also show that equilibrium payoffs are unique, unless valuation of at least one of the players is an even integer number. If equilibrium payoffs are not unique, continuum of equilibrium payoffs are possible. We compare equilibrium characterization and equilibrium payoffs with the continuous variant of all-pay auctions.

翻译：我们研究了完全信息下离散两位玩家全支付拍卖。我们完整刻画了混合策略纳什均衡，并证明这些均衡构成离散型General Lotto博弈纳什均衡的子集。研究表明，尽管均衡通常不唯一，但具有可互换性。我们还证明了除非至少一位玩家的估值为偶数整数，否则均衡收益是唯一的。当均衡收益不唯一时，可能存在连续区间内的均衡收益。我们将均衡刻画及均衡收益与连续型全支付拍卖进行了比较。