Common-value all-pay auctions with asymmetric information

We study two-player common-value all-pay auctions in which the players have ex-ante asymmetric information represented by finite connected partitions of the set of states of nature. Our focus is on a family of such auctions in which no player has an information advantage over his opponent. We find sufficient conditions for the existence of equilibrium with monotone strategies, and show that such an equilibrium is unique. We further show that the ex-ante distribution of equilibrium effort is the same for every player (and hence the players’ expected efforts are equal), although their expected payoffs are different and they do not have the same ex-ante probability of winning.