Regularity Theory for Mean-Field Game Systems

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On non-uniqueness and uniqueness of solutions in finite-horizon Mean Field Games (2017, unknown): “General presentations of the ﬁeld are [10, 26, 27], and many applications are analysed in [24, 30].”
Finite Mean Field Games: Fictitious play and convergence to a first order continuous mean field game (2018, background): “Lions [25] and to [9, 19, 18, 17] for surveys on the theory and its applications.”
Mean field games models of segregation (2016, background): “[32]), and finely combine regularity of the HJB equation and the Fokker-Planck equation to prove existence of solutions of (27), at least if the space dimension is sufficiently small (d = 1, 2).”
Nonlinear elliptic systems and mean-field games (2016, methodology): “For a general presentations of Mean-Field Games and their applications we refer to the lecture notes by Guéant, Lasry, and Lions [40] and Cardaliaguet [22], the survey paper [39] and the very recent books [35,37] by Gomes and collaborators.”