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Mean-field games with a major player. (Jeux à champ moyen avec agent dominant.) (English. Abridged French version) Zbl 1410.91048
Summary: We introduce and study mathematically a new class of mean-field-game systems of equations. This class of equations allows us to model situations involving one major player (or agent) and a “large” group of “small” players.

MSC:
91A15 Stochastic games, stochastic differential games
91A23 Differential games (aspects of game theory)
91A13 Games with infinitely many players (MSC2010)
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[1] Bensoussan, A.; Chau, M. H.M.; Yan, S. C.P., Mean field games with a dominating player, (2014) · Zbl 1348.49031
[2] Cardaliaguet, P., Notes on mean field games, (2013), PDF file at · Zbl 1314.91043
[3] Carmona, R.; Delarue, F., Probabilistic theory of mean field games with applications I-II, (2018), Springer · Zbl 1422.91014
[4] Huang, M.; Malhamé, P. P.; Gaines, P. E., Large population stochastic dynamics games, Commun. Inf. Syst., 6, 221-252, (2006)
[5] Krusell, P.; Sinith, A. D., Income and wealth heterogeneity in the macroeconomy, J. Polit. Econ., 106, 867-896, (1998)
[6] Lasry, J-M.; Lions, P-L., Jeux à champ moyen I. le cas stationnaire, C. R. Acad. Sci. Paris, Ser. I, 343, 619-625, (2006) · Zbl 1153.91009
[7] Lasry, J-M.; Lions, P-L., Jeux à champ moyen II. horizon fini et contrôle optimal, C. R. Acad. Sci. Paris, Ser. I, 343, 679-684, (2006) · Zbl 1153.91010
[8] Lasry, J-M.; Lions, P-L., Mean field games, Jpn. J. Math., 2, 229-260, (2007) · Zbl 1156.91321
[9] Lions, P-L., (2007-2012), Videos and abstracts at
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