A Probabilistic Approach to Discounted Infinite Horizon and Invariant Mean Field Games
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910512924590080 |
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| author | Carmona, René Tangpi, Ludovic Zhang, Kaiwen |
| author_facet | Carmona, René Tangpi, Ludovic Zhang, Kaiwen |
| contents | This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove existence and uniqueness of solutions for the extended infinite horizon game. The key idea is to construct local versions of the previously considered stable topologies. Further, we analyze how sequences of finite horizon games approximate the infinite horizon one. Under a weakened Lasry-Lions monotonicity condition, we can quantify the convergence rate of solutions for the finite horizon games to the one for the infinite horizon game using a novel stability result for mean field games. Lastly, applying our results allows to solve the invariant mean field game as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Probabilistic Approach to Discounted Infinite Horizon and Invariant Mean Field Games Carmona, René Tangpi, Ludovic Zhang, Kaiwen Optimization and Control Probability This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove existence and uniqueness of solutions for the extended infinite horizon game. The key idea is to construct local versions of the previously considered stable topologies. Further, we analyze how sequences of finite horizon games approximate the infinite horizon one. Under a weakened Lasry-Lions monotonicity condition, we can quantify the convergence rate of solutions for the finite horizon games to the one for the infinite horizon game using a novel stability result for mean field games. Lastly, applying our results allows to solve the invariant mean field game as well. |
| title | A Probabilistic Approach to Discounted Infinite Horizon and Invariant Mean Field Games |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2407.03642 |