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

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Détails bibliographiques
Auteurs principaux:	Décamps, Jean-Paul, Gensbittel, Fabien, Mariotti, Thomas
Format:	Preprint
Publié:	2024
Sujets:	Optimization and Control
Accès en ligne:	Acceder al recurso
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author	Décamps, Jean-Paul Gensbittel, Fabien Mariotti, Thomas
author_facet	Décamps, Jean-Paul Gensbittel, Fabien Mariotti, Thomas
contents	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. The proof uses the fact that the space of Markovian randomized stopping times can be topologized as a compact absolute retract, which in turn enables us to use a powerful fixed-point theorem by Eilenberg and Montgomery. We illustrate our results with an example of a war of attrition that admits a mixed-strategy Markov-perfect equilibrium but no pure-strategy Markov-perfect equilibrium.
format	Preprint
id	arxiv_https___arxiv_org_abs_2407_04878
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition Décamps, Jean-Paul Gensbittel, Fabien Mariotti, Thomas Optimization and Control 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. The proof uses the fact that the space of Markovian randomized stopping times can be topologized as a compact absolute retract, which in turn enables us to use a powerful fixed-point theorem by Eilenberg and Montgomery. We illustrate our results with an example of a war of attrition that admits a mixed-strategy Markov-perfect equilibrium but no pure-strategy Markov-perfect equilibrium.
title	Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition
topic	Optimization and Control
url	https://arxiv.org/abs/2407.04878

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