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In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework that is particularly convenient for these problems.
Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
M. Bardi and I. Capuzzo-Dolcetta · 1997
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Topics in optimal transportation
C. Villani · 2003
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Controlled Markov processes and viscosity solutions
W. H. Fleming and H. M. Soner · 2006
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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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J.-M. Lasry and P.-L. Lions · 2006
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Jeux à champ moyen. II. Horizon fini et contrôle optimal
J.-M. Lasry and P.-L. Lions · 2006
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Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ϵ \epsilon -Nash equilibria
M. Huang, P. E. Caines, and R. P. Malhamé · 2007
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J.-M. Lasry and P.-L. Lions · 2007
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R. Carmona, F. Delarue, and D. Lacker · 2013
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Second order mean field games with degenerate diffusion and local coupling
P. Cardaliaguet, P. Garber, A. Porretta, and D. Tonon · 2014
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On the existence of classical solutions for stationary extended mean field games
D. Gomes, S. Patrizi, and V. Voskanyan · 2014
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Time dependent mean-field games with logarithmic nonlinearities
D. Gomes and E. Pimentel · 2014
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Mean field games models—a brief survey
D. Gomes and J. Saúde · 2014
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Local regularity for mean-field games in the whole space
D. Gomes and E. Pimentel · 2015
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Time-dependent mean-field games in the subquadratic case
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Time dependent mean-field games in the superquadratic case
D. Gomes, E. Pimentel, and H. Sánchez-Morgado
Cited in the paper.
Weak solutions to Fokker-Planck equations and mean field games
A. Porretta · 2015
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