Remarks on potential mean field games
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909433564495872 |
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| author | Graber, P. Jameson |
| author_facet | Graber, P. Jameson |
| contents | In this expository article, we give an overview of the concept of potential mean field games of first order. We give a new proof that minimizers of the potential are equilibria by using a Lagrangian formulation. We also provide criteria to determine whether or not a game has a potential. Finally, we discuss in some depth the selection problem in mean field games, which consists in choosing one out of multiple Nash equilibria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on potential mean field games Graber, P. Jameson Analysis of PDEs Optimization and Control 35Q89, 49N80, 91A16 In this expository article, we give an overview of the concept of potential mean field games of first order. We give a new proof that minimizers of the potential are equilibria by using a Lagrangian formulation. We also provide criteria to determine whether or not a game has a potential. Finally, we discuss in some depth the selection problem in mean field games, which consists in choosing one out of multiple Nash equilibria. |
| title | Remarks on potential mean field games |
| topic | Analysis of PDEs Optimization and Control 35Q89, 49N80, 91A16 |
| url | https://arxiv.org/abs/2405.15921 |