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.
war of attrition, exit, rent seeking, auctions, stochastic dominance, games of timing, bargaining, voluntary provision of public goods, macroeconomics stabilization, adoption of technological standards
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