On weak solutions to first-order discount mean field games

Abstract

In this paper, 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.

26 pages, 2 figures

References in corpus (2)

• Convergence of the solutions of the discounted equation: the discrete case
• Convergence of the solutions of the MFG discounted Hamilton-Jacobi equation