Mixed Markov-Perfect Equilibria in the Continuous-Time War of Attrition
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916849316265984 |
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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 |