Instant Exit from the Asymmetric War of Attrition

In an asymmetric war of attrition the players` prize valuations are drawn from different distributions. A stochastic strength ordering, based upon relative hazard rates, is used to rank these distributions. The stochastically stronger player is perceived to be strong ex ante, even though her realized valuation may be lower ex post. Since the classic war of attrition exhibits multiple equilibria, the game is perturbed; for instance, by imposing an arbitrarily large time limit, or allowing for the arbitrarily small probability of players that are restricted to fighting forever. In the unique equilibrium of the perturbed game, a stochastically weaker player almost always instantly exits at the beginning, even though her valuation may be higher.