Weakly coupled mean-field game systems

TL;DR

This paper establishes the existence of solutions for first-order mean-field games related to optimal switching by employing penalization, uniform estimates, and limiting procedures.

Contribution

It introduces a novel approach combining penalization and limiting techniques to prove existence in first-order MFGs with optimal switching.

Findings

Existence of solutions to first-order MFGs with optimal switching proven.

Development of a penalization method for approximate solutions.

Uniform estimates established for the penalized problem.

Abstract

Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem.