The Absence of Attrition in the War of Attrition under Complete Information
36 Pages Posted: 8 Apr 2019 Last revised: 30 Nov 2021
Date Written: November 10, 2021
We consider a two-player game of war of attrition under complete information. It is well- known that this class of games admits equilibria in pure, as well as mixed strategies, and much of the literature has focused on the latter. We show that if the players’ payoffs whilst in “war” vary stochastically and their exit payoffs are heterogeneous, then the game admits Markov Perfect equilibria in pure strategies only. This is true 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, the game admits equilibria in pure and mixed strategies.
Keywords: war of attrition, stochastic dynamic game, equilibrium selection
JEL Classification: C73, C72
Suggested Citation: Suggested Citation