Coarse correlated equilibria for continuous time mean field games in open loop strategies
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917874721882112 |
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| author | Campi, Luciano Cannerozzi, Federico Fischer, Markus |
| author_facet | Campi, Luciano Cannerozzi, Federico Fischer, Markus |
| contents | In the framework of continuous time symmetric stochastic differential games in open loop strategies, we introduce a generalization of mean field game solution, called coarse correlated solution. This can be seen as the analogue of a coarse correlated equilibrium in the $N$-player game, where a moderator randomly generates a strategy profile and asks the players to pre-commit to such strategies before disclosing them privately to each one of them; such a profile is a coarse correlated equilibrium if no player has an incentive to unilaterally deviate. We justify our definition by showing that a coarse correlated solution for the mean field game induces a sequence of approximate coarse correlated equilibria with vanishing error for the underlying $N$-player games. Existence of coarse correlated solutions for the mean field game is proved by means of a minimax theorem. An example with explicit solutions is discussed as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16728 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Coarse correlated equilibria for continuous time mean field games in open loop strategies Campi, Luciano Cannerozzi, Federico Fischer, Markus Probability Optimization and Control In the framework of continuous time symmetric stochastic differential games in open loop strategies, we introduce a generalization of mean field game solution, called coarse correlated solution. This can be seen as the analogue of a coarse correlated equilibrium in the $N$-player game, where a moderator randomly generates a strategy profile and asks the players to pre-commit to such strategies before disclosing them privately to each one of them; such a profile is a coarse correlated equilibrium if no player has an incentive to unilaterally deviate. We justify our definition by showing that a coarse correlated solution for the mean field game induces a sequence of approximate coarse correlated equilibria with vanishing error for the underlying $N$-player games. Existence of coarse correlated solutions for the mean field game is proved by means of a minimax theorem. An example with explicit solutions is discussed as well. |
| title | Coarse correlated equilibria for continuous time mean field games in open loop strategies |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2303.16728 |