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

Author

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  • Jean-Paul Décamps

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université 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 - UT - Université 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)

  • Fabien Gensbittel

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université 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)

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 [16] 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.

Suggested Citation

  • Jean-Paul Décamps & Thomas Mariotti & Fabien Gensbittel, 2024. "Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition," Working Papers hal-04748393, HAL.
    • Handle: RePEc:hal:wpaper:hal-04748393
    Note: View the original document on HAL open archive server: https://hal.science/hal-04748393v1
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    References listed on IDEAS

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    1. Andrew McLennan, 2018. "Advanced Fixed Point Theory for Economics," Springer Books, Springer, number 978-981-13-0710-2, June.
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