Calculus of Variations and Geometric Measure Theory
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Y. Achdou - M. Bardi - M. Cirant

Mean Field Games models of segregation

created by bardi on 16 Jul 2016
modified on 09 Mar 2017


Published Paper

Inserted: 16 jul 2016
Last Updated: 9 mar 2017

Journal: Math. Models Methods Appl. Sci.
Volume: 27
Number: 1
Pages: 75--113
Year: 2017
Doi: 10.1142/S0218202517400036


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.

Keywords: Mean Field Games, multi-populations models, large populations limit, systems of parabolic equations, segregation, finite difference methods


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