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Minimax Theory and its Applications 07 (2022), No. 1, 001--055
Copyright Heldermann Verlag 2022

Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations

Masaaki Fujii
Quantitative Finance Course, Graduate School of Economics, University of Tokyo, Japan

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.

Keywords: Mean field game, mean field type control, FBSDE of McKean-Vlasov type.

MSC: 60H10, 91A13, 91A15, 93E20.

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