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

Jean-Paul Décamps, Thomas Mariotti and Fabien Gensbittel

No 24-1562, TSE Working Papers from Toulouse School of Economics (TSE)

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.

Keywords: War of Attrition; Markovian Randomized Stopping Time; Markov-Perfect Equilibrium; Fixed-Point Theorem. (search for similar items in EconPapers)
Date: 2024-08
New Economics Papers: this item is included in nep-gth and nep-mic
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Working Paper: Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition (2024)
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