When Bidding More is Not Enough: All-Pay Auctions with Handicaps

We consider a standard two-player all-pay auction with private values, where the valuation for the object is private information to each bidder. The crucial feature is that one bidder is favored by the allocation rule in the sense that he need not bid as much as the other bidder to win the auction. Analogously, the other bidder is handicapped by the rule as overbidding the rival may not be enough to win the auction. Clearly, this has important implications on equilibrium behavior. We fully characterize the equilibrium strategies for this auction format and show that there exists a unique pure strategy Bayesian Nash Equilibrium.