Uniqueness of solutions in Mean Field Games with several populations and Neumann conditions

TL;DR

This paper investigates the conditions under which solutions to multi-population Mean Field Game systems with Neumann boundary conditions are unique, focusing on small data assumptions like short time horizons, and extends previous existence results.

Contribution

It provides new uniqueness results for multi-population MFG systems with Neumann conditions under small data assumptions, complementing earlier existence findings.

Findings

Uniqueness holds when certain data, such as the time horizon, are sufficiently small.

The results extend to applications in robust Mean Field Games.

The study complements existing existence results for segregation models.

Abstract

We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time horizon. This complements the existence results for MFG models of segregation phenomena introduced by the authors and Achdou. An application to robust Mean Field Games is also given.