On Approximate Nash Equilibria in Mean Field Games
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914288828940288 |
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| author | Djete, Mao Fabrice Touzi, Nizar |
| author_facet | Djete, Mao Fabrice Touzi, Nizar |
| contents | In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under such strategies converges to zero in the large population size asymptotic. We show that these strategies satisfy an $Ł^\infty$ notion of approximate Nash equilibrium which guarantees that the individual gain from optimal unilateral deviation is small uniformly among players and uniformly on their initial characteristics. We establish these results in the context of static models and in the dynamic continuous time setting, and we cover situations where the agents' criteria depend on the conditional law of the controlled state process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20910 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Approximate Nash Equilibria in Mean Field Games Djete, Mao Fabrice Touzi, Nizar Computer Science and Game Theory Optimization and Control Probability In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under such strategies converges to zero in the large population size asymptotic. We show that these strategies satisfy an $Ł^\infty$ notion of approximate Nash equilibrium which guarantees that the individual gain from optimal unilateral deviation is small uniformly among players and uniformly on their initial characteristics. We establish these results in the context of static models and in the dynamic continuous time setting, and we cover situations where the agents' criteria depend on the conditional law of the controlled state process. |
| title | On Approximate Nash Equilibria in Mean Field Games |
| topic | Computer Science and Game Theory Optimization and Control Probability |
| url | https://arxiv.org/abs/2601.20910 |