Geodesic
Probabilistic approach to mean field games and mean field type control problems with multiple populations
Minimax theory and its applications, Tome 7 (2022) no. 1
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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.
Mots-clés : Mean field game, mean field type control, FBSDE of McKean-Vlasov type 
@article{MTA_2022_7_1_a0,
     author = {Masaaki Fujii},
     title = {Probabilistic approach to mean field games and mean field type control problems with multiple populations},
     journal = {Minimax theory and its applications},
     year = {2022},
     volume = {7},
     number = {1},
     zbl = {1492.91043},
     url = {http://geodesic.mathdoc.fr/item/MTA_2022_7_1_a0/}
}
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Masaaki Fujii. Probabilistic approach to mean field games and mean field type control problems with multiple populations. Minimax theory and its applications, Tome 7 (2022) no. 1. http://geodesic.mathdoc.fr/item/MTA_2022_7_1_a0/