Décamps, Jean-Paul, Gensbittel, Fabien and Mariotti, Thomas (2026) Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition. Annals of Applied Probability, Vol. 36 (n°2). pp. 1769-1814.

Abstract

We prove the existence of a Markov-perfect equilibrium in randomized stopping times for a model of the war of attrition in which the underlying state variable follows a homogenous linear diffusion. We first prove that the space of Markovian randomized stopping times can be topologized as a compact absolute retract. This in turn enables us to use a powerful fixed-point theorem by Eilenberg and Montgomery [22] to prove our existence theorem. We illustrate our results with an example of a war of attrition that admits a mixed-strategy Markov-perfect equilibrium but no pure-strategy Markovperfect
equilibrium.

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