Ergodic Mean Field Games of Controls with State Constraints
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917392439836672 |
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| author | Graber, Jameson Rosengartner, Kyle |
| author_facet | Graber, Jameson Rosengartner, Kyle |
| contents | In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints, in which equilibria are characterized by solutions to a second-order MFGC system where the value function blows up at the boundary, the density of players vanishes at a commensurate rate, and the joint distribution of states and controls satisfies the appropriate fixed-point relation. We prove that such systems are well-posed in the case of monotone coupling and Hamiltonians with at most quadratic growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ergodic Mean Field Games of Controls with State Constraints Graber, Jameson Rosengartner, Kyle Analysis of PDEs Optimization and Control In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints, in which equilibria are characterized by solutions to a second-order MFGC system where the value function blows up at the boundary, the density of players vanishes at a commensurate rate, and the joint distribution of states and controls satisfies the appropriate fixed-point relation. We prove that such systems are well-posed in the case of monotone coupling and Hamiltonians with at most quadratic growth. |
| title | Ergodic Mean Field Games of Controls with State Constraints |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2604.07550 |