Geodesic
On weak solutions to first-order discount mean field games
Minimax theory and its applications, Tome 8 (2023) no. 1
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We establish the existence and uniqueness of weak solutions to first-order discount mean field games and a stability result to give the existence for the ergodic problem. We show an example to illustrate the multiplicity of weak solutions to the ergodic problem. With this motivation, we address a selection condition, which is a necessary condition that any limit of solutions under subsequence satisfies. As an application, we show a nontrivial example to get the convergence of weak solutions.
Mots-clés : Mean field games, ergodic problem, vanishing discount approximation 
@article{MTA_2023_8_1_a6,
     author = {Hiroyoshi Mitake and Kengo Terai},
     title = {On weak solutions to first-order discount mean field games},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {1},
     zbl = {1520.35153},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a6/}
}
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Hiroyoshi Mitake; Kengo Terai. On weak solutions to first-order discount mean field games. Minimax theory and its applications, Tome 8 (2023) no. 1. http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a6/