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