The Absence of Attrition in a War of Attrition under Complete Information

We consider a two-player game of war of attrition under complete information. Our main result shows that if the players' payoffs whilst fighting for the prize vary stochastically, and their exit payoffs are heterogeneous, then the game admits Markov Perfect equilibria in pure strategies only. This result holds irrespective of the degree of randomness and heterogeneity, thus highlighting the fragility of mixed-strategy equilibria to a natural perturbation of the canonical model. In contrast, when the players' flow payoffs are deterministic or their exit payoffs are homogeneous, we show that the game admits equilibria in pure, as well as in mixed strategies.