Memoryless-Strategy Equilibria of a <i>N</i>-Player War of Attrition Game with Complete Information

Abstract Consider a war of attrition game in continuous time with complete information, in which N ≥ 2 players compete for N − K prizes. I focus on the equilibria in which the strategies follow exponential distributions, which are memoryless. When K = 1, such an equilibrium can be explicitly characterized. The equilibrium certainly exists if N = 2. If N ≥ 3, it exists as long as the weakest player is not too weak compared to the average. If it exists, the equilibrium is unique under some conditions. When K ≥ 2, the game typically has nondegenerate equilibria in which K − 1 relatively weak players concede at the beginning. The model can be extended to the case in which the players have loser-dependent valuations. The model helps to solve a generalized exit game in a “nature oligopoly” and an all-pay auction with ascending bids.