N-Player War of Attrition with Complete Information

This paper generalises the classic two-player war of attrition game with complete information to a game in which N heterogeneous players compete for N − K prizes. The game with K = 1 may have a nondegenerate equilibrium in which the players’ strategies follow exponential distributions. The equilibrium surely exists in the classic case (with N = 2 and K = 1), but when N ≥ 3 and K = 1, it exists only when the weakest player is not too weak. When K ≥ 2, the game typically has multiple nondegenerate equilibria in which K −1 players exit immediately. The model can be extended to the case where winners’ payoffs depend on which players lose, or where players face randomly arriving ‘defeats’. The findings can be applied to an all-pay auction with ascending bids