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 partitions of the set of possible values of winning. We consider two families of such auctions: in the first, one of the players has an information advantage (henceforth, IA) over his opponent, and in the second, no player has an IA over his opponent. We show that there exists a unique equilibrium in auctions with IA and explicitly characterize it; for auctions without IA we find a sufficient condition for the existence of equilibrium in monotonic strategies. We further show that, with or without IA, 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. In auctions with IA, the players have the same ex-ante probability of winning, which is not the case in auctions without IA.