Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition
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...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2407.04878 |