The convergence problem in mean field games with a local coupling

TL;DR

This paper investigates how a system of coupled Hamilton-Jacobi equations converges to a mean field game system with local coupling as the number of players grows large, especially under increasingly singular interactions.

Contribution

It provides a rigorous analysis of the convergence of the Nash system to the mean field game system with local coupling in the presence of singular interactions.

Findings

Established convergence of the Nash system to the mean field limit.

Analyzed the impact of singular coupling on the convergence process.

Extended the understanding of local coupling effects in mean field games.

Abstract

The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations (the Nash system) when the coupling between the players becomes increasingly singular. The limit equation is a mean field game system with local coupling.