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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2502.12389 |
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| _version_ | 1866910834358222848 |
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| author | Cont, Rama Hu, Anran |
| author_facet | Cont, Rama Hu, Anran |
| contents | We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations. We consider strategic interactions in a population of players which may be partitioned into near-homogeneous sub-populations subject to peer group effects and interactions across groups. We prove a quantitative homogenization result for multi-player games in this setting: we show that $ε$-Nash equilibria of a general multi-player game with heterogeneity may be computed in terms of the Nash equilibria of an auxiliary multi-population mean-field game. We provide explicit and non-asymptotic bounds for the distance from optimality in terms of the number of players and the deviations from homogeneity in sub-populations. The best mean-field approximation corresponds to an optimal partition into sub-populations, which may be formulated as the solution of a mixed-integer program. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homogenization and Mean-Field Approximation for Multi-Player Games Cont, Rama Hu, Anran Optimization and Control We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations. We consider strategic interactions in a population of players which may be partitioned into near-homogeneous sub-populations subject to peer group effects and interactions across groups. We prove a quantitative homogenization result for multi-player games in this setting: we show that $ε$-Nash equilibria of a general multi-player game with heterogeneity may be computed in terms of the Nash equilibria of an auxiliary multi-population mean-field game. We provide explicit and non-asymptotic bounds for the distance from optimality in terms of the number of players and the deviations from homogeneity in sub-populations. The best mean-field approximation corresponds to an optimal partition into sub-populations, which may be formulated as the solution of a mixed-integer program. |
| title | Homogenization and Mean-Field Approximation for Multi-Player Games |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.12389 |