Mean Field Games of Controls with Boundary Conditions & Invariance Constraints
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918230655762432 |
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| author | Graber, P. Jameson Rosengartner, Kyle |
| author_facet | Graber, P. Jameson Rosengartner, Kyle |
| contents | In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of controls in which the value function and the distribution of player states satisfy either Dirichlet or Neumann boundary conditions. We prove that such systems are well-posed either with sufficient smallness conditions or in the case of monotone couplings. Next, we consider mean field games of controls under invariance constraints imposed on the state space. We prove the existence and uniqueness of weak solutions to our mean field game system, and then we prove higher regularity of solutions under some additional assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean Field Games of Controls with Boundary Conditions & Invariance Constraints Graber, P. Jameson Rosengartner, Kyle Optimization and Control Analysis of PDEs In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of controls in which the value function and the distribution of player states satisfy either Dirichlet or Neumann boundary conditions. We prove that such systems are well-posed either with sufficient smallness conditions or in the case of monotone couplings. Next, we consider mean field games of controls under invariance constraints imposed on the state space. We prove the existence and uniqueness of weak solutions to our mean field game system, and then we prove higher regularity of solutions under some additional assumptions. |
| title | Mean Field Games of Controls with Boundary Conditions & Invariance Constraints |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2508.21642 |