This paper proves the existence of the optimal all-pay auction when signals are correlated. In an all-pay auction every bidder pays his bid. The war of attrition is an auction in which every bidder but the winner pays his bid. The winner pays the second highest bid. Recently Krishna and Morgan showed that the war of attrition, if signals are correlated, dominates the all-pay auction. Examples in the paper show that the optimal all-pay auction may be optimal among all auctions and may dominate the war of attrition.
all-pay auction; correlated signals
