Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition

Jean-Paul Décamps, Fabien Gensbittel and Thomas Mariotti
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Jean-Paul Décamps: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, TSM - Toulouse School of Management Research - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - CNRS - Centre National de la Recherche Scientifique - TSM - Toulouse School of Management - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse
Fabien Gensbittel: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Thomas Mariotti: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: War of Attrition; Markovian Randomized Stopping Time; Markov-Perfect Equilibrium; Fixed-Point Theorem. (search for similar items in EconPapers)
Date: 2026-04
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Published in The Annals of Applied Probability, 2026, Vol. 36 (n°2), pp.1769-1814. ⟨10.1214/25-AAP2270⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05615313

DOI: 10.1214/25-AAP2270

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