Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2304.09509 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914715103395840 |
|---|---|
| author | Bardi, Martino Kouhkouh, Hicham |
| author_facet | Bardi, Martino Kouhkouh, Hicham |
| contents | We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such a cost has an equilibrium, and we build from it a solution of the ergodic MFG system of 1st order PDEs with the same cost. Next we address the long-time limit of the solutions to finite horizon MFG with cost functional satisfying various additional assumptions, but not the classical Lasry-Lions monotonicity condition. Instead we assume that the cost has the same set of minima for all measures describing the population. We prove the convergence of the distribution of the agents and of the value function to a solution of the ergodic MFG system as the horizon of the game tends to infinity, extending to this class of MFG some results of weak KAM theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09509 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Long-time behaviour of deterministic Mean Field Games with non-monotone interactions Bardi, Martino Kouhkouh, Hicham Analysis of PDEs Optimization and Control 35Q89, 35B40, 35F21, 91A16 We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such a cost has an equilibrium, and we build from it a solution of the ergodic MFG system of 1st order PDEs with the same cost. Next we address the long-time limit of the solutions to finite horizon MFG with cost functional satisfying various additional assumptions, but not the classical Lasry-Lions monotonicity condition. Instead we assume that the cost has the same set of minima for all measures describing the population. We prove the convergence of the distribution of the agents and of the value function to a solution of the ergodic MFG system as the horizon of the game tends to infinity, extending to this class of MFG some results of weak KAM theory. |
| title | Long-time behaviour of deterministic Mean Field Games with non-monotone interactions |
| topic | Analysis of PDEs Optimization and Control 35Q89, 35B40, 35F21, 91A16 |
| url | https://arxiv.org/abs/2304.09509 |