Minimax Theory and its Applications 08 (2023), No. 1, 139--170
Copyright Heldermann Verlag 2023
On Weak Solutions to First-Order Discount Mean Field Games
Hiroyoshi Mitake
Graduate School of Mathematical Sciences, The University of Tokyo, Japan
mitake@ms.u-tokyo.ac.jp
Kengo Terai
Graduate School of Mathematical Sciences, The University of Tokyo, Japan
terai@ms.u-tokyo.ac.jp
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.
Keywords: Mean field games, ergodic problem, vanishing discount approximation.
MSC: 35A01, 91A13, 49L25.
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