MEAN FIELD GAMES MODELS OF SEGREGATION

Yves Achdou (1) , Martino Bardi (2) , Marco Cirant (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Unipd - Università degli Studi di Padova = University of Padua

This paper introduces and analyzes 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.

Mots clés: Mean Field Games; multi-populations models; large populations limit; sys-; systems of parabolic equations; finite difference methods; segregation; 49N70; 35K55

Domaines: Analyse numérique [cs.NA]

Yves Achdou, Martino Bardi, Marco Cirant. MEAN FIELD GAMES MODELS OF SEGREGATION. 2016. ⟨hal-01412582⟩