Discussion Papers 2019

CIRJE-F-1133	"Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations"
Author Name	Fujii, Masaaki
Date	November 2019
Full Paper	PDF File
Remarks	Reviced in December 2019 and November 2020. Forthcoming in Minimax Theory and its Applications.

Abstract
In this work, we systematically investigate mean field games and mean field type control problems with multiple populations. We study the mean field limits of the three different situations; (i) every agent is non-cooperative; (ii) the agents within each population are cooperative; and (iii) the agents in some populations are cooperative. We provide several sets of sufficient conditions for the existence of a mean field equilibrium for each case. We also show that, under appropriate conditions, each mean field solution actually provides an approximate Nash equilibrium for the corresponding game with a large but finite number of agents.

Abstract

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations. We study the mean field limits of the three different situations; (i) every agent is non-cooperative; (ii) the agents within each population are cooperative; and (iii) the agents in some populations are cooperative. We provide several sets of sufficient conditions for the existence of a mean field equilibrium for each case. We also show that, under appropriate conditions, each mean field solution actually provides an approximate Nash equilibrium for the corresponding game with a large but finite number of agents.