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Probabilistic approach to mean field games and mean field type control problems with multiple populations. (English) Zbl 1492.91043

Summary: 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.

MSC:

91A16 Mean field games (aspects of game theory)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E20 Optimal stochastic control
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