Mean Field Games models of segregation

TL;DR

This paper develops and analyzes Mean Field Game models to understand segregation phenomena between two populations, providing theoretical results, numerical methods, and simulations inspired by urban settlement studies.

Contribution

It introduces new Mean Field Game models for segregation, proves large population limits, establishes existence of solutions, and offers numerical simulations.

Findings

Segregation phenomena are demonstrated in simulations.

Large population limits are rigorously proved.

Existence of solutions for the differential game systems is established.

Abstract

This paper introduces and analyses some models in the framework of Mean Field Games describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games, a large population limit is proved. For differential games with noise, the existence of solutions is established for the systems of partial differential equations of Mean Field Game theory, in the stationary and in the evolutive case. Numerical methods are proposed, with several simulations. In the examples and in the numerical results, particular emphasis is put on the phenomenon of segregation between the populations.