Common-Value All-Pay Auctions with Asymmetric Information and Bid Caps

We study two-player common-value all-pay auctions (contests) with asymmetric information under the assumption that one of the players has an information advantage over his opponent and both players are budget-constrained. We generalize the results for all-pay auctions with complete information, and show that in all-pay auctions with asymmetric information, sufficiently high (but still binding) bid caps do not change the players' expected total effort compared to the benchmark auction without any bid cap. Furthermore, we show that there are bid caps that increase the players' expected total effort compared to the benchmark. Finally, we demonstrate that there are bid caps which may have an unanticipated effect on the players' expected payoffs – one player's information advantage may turn into a disadvantage as far as his equilibrium payoff is concerned.