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

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

No CARF-F-497, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

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.

Pages: 51
Date: 2020-11
New Economics Papers: this item is included in nep-gth
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