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We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France.
Topics in propagation of chaos
A.S. Sznitman · 1989
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Stochastic Hamilton Jacobi Bellman equations
S. Peng · 1992
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The Malliavin Calculus and Related Topics
D. Nualart · 1995
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Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
M. Huang, P.E. Caines, and R.P. Malhamé · 2006
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Jeux à champ moyen I. Le cas stationnaire
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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Théorie des jeux à champs moyen et applications
P.L. Lions · 2008
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O. Guéant, J.M. Lasry, and P.L. Lions · 2010
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Notes on mean field games
P. Cardaliaguet · 2012
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Mean field games with a common noise
R. Carmona, F. Delarue, and D. Lacker
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Mean Field Games and Systemic Risk
R. Carmona, J.P. Fouque, and A. Sun
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On non-Markovian forward-backward SDEs and backward stochastic PDEs
J. Ma, H. Yin and J. Zhang · 2012
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Probabilistic analysis of mean field games
R. Carmona and F. Delarue · 2013
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Control of McKean-Vlasov versus Mean Field Games
R. Carmona, F. Delarue, and A. Lachapelle · 2013
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Mean field games models - a brief survey
D.A. Gomes and J. Saude · 2013
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Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics
R. Carmona and F. Delarue · 2014
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McKean-Vlasov FBSDEs and related Master Equation
J.F. Chassagneux, D. Crisan, and F. Delarue
Cited in the paper.