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

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  • Décamps, Jean-Paul
  • Mariotti, Thomas
  • Gensbittel, Fabien

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

  • Décamps, Jean-Paul & Mariotti, Thomas & Gensbittel, Fabien, 2024. "Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition," TSE Working Papers 24-1562, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:129668
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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, September.
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    More about this item

    Keywords

    War of Attrition; Markovian Randomized Stopping Time; Markov-Perfect Equilibrium; Fixed-Point Theorem.;
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