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Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$.
Fixed-point and minimax theorems in locally convex topological linear spaces
K. Fan · 1952
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A class of Markov processes associated with nonlinear parabolic equations
H. P. McKean · 1966
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Convergence of Probability Measures
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Multidimensional Diffusion Processes , volume 233 of Grundlehren der mathematischen Wissenschaften
D. W. Stroock and S. R. S. Varadhan · 1979
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A certain class of diffusion processes associated with nonlinear parabolic equations
T. Funaki · 1984
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A martingale approach to the law of large numbers for weakly interacting stochastic processes
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Compactification methods in the control of degenerate diffusions: existence of an optimal control
N. El Karoui, D. H. Nguyen, and M. Jeanblanc-Picqué · 1987
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Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems , volume 3 of Systems & Control: Foundations & Applications
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Brownian Motion and Stochastic Calculus , volume 113 of Graduate Texts in Mathematics
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Topics in propagation of chaos
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Stochastic Optimal Control: The Discrete-Time Case
D. P. Bertsekas and S. E. Shreve · 1996
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On the existence of universal functional solutions to classical SDEs
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Markov transitions and the propagation of chaos
A. D. Gottlieb · 1998
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Foundations of Modern Probability
O. Kallenberg · 2001
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Topics in Optimal Transportation , volume 58 of Graduate Studies in Mathematics
Mean field games and nonlinear Markov processes
V. N. Kolokoltsov, J. Li, and W. Yang · 2011
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Large deviation properties of weakly interacting processes via weak convergence methods
A. Budhiraja, P. Dupuis, and M. Fischer · 2012
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LQG mean-field games with ergodic costs
M. Bardi and F. S. Priuli · 2013
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Notes on mean field games
P. Cardaliaguet · 2013
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Probabilistic analysis of mean-field games
R. Carmona and F. Delarue · 2013
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Control of McKean-Vlasov dynamics versus mean field games
R. Carmona, F. Delarue, and A. Lachapelle · 2013
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C. Villani · 2003
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Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
M. Huang, R. P. Malhamé, and P. E. Caines · 2006
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Mean field games
J.-M. Lasry and P.-L. Lions · 2007
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On the moments of the modulus of continuity of Itô processes
M. Fischer and G. Nappo · 2010
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Mean field games via controlled martingale problems: existence of Markovian equilibria
D. Lacker
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A general characterization of the mean field limit for stochastic differential games
D. Lacker
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The derivation of ergodic mean field game equations for several populations of players
E. Feleqi · 2013
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Continuous time finite state mean field games
D. A. Gomes, J. Mohr, and R. R. Souza · 2013
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Linear-quadratic N N -person and mean-field games with ergodic cost
M. Bardi and F. S. Priuli · 2014
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A probabilistic weak formulation of mean field games and applications
R. Carmona and D. Lacker · 2015
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