Mean field games: the master equation and the mean field limit
Pierre Cardaliaguet1
1 Ceremade, Université Paris-Dauphine France
Séminaire Laurent Schwartz — EDP et applications (2015-2016), Talk no. 17, 10 p.

We present here results obtained in the joint work with Delarue, Lasry and Lions [4] on the convergence, as N tends to infinity, of a system of N coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. The limit problem can be expressed in terms of the “Mean Field Game” system (coupling a Hamilton-Jacobi equation with a Fokker-Planck equation), or, alternatively, in terms of the “master equation” (a kind of second order partial differential equation stated on the space of probability measures). We also discuss the behavior of the optimal trajectories, for which we show a propagation of chaos property.

Published online:
DOI: 10.5802/slsedp.99
Pierre Cardaliaguet 1

1 Ceremade, Université Paris-Dauphine France 
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Pierre Cardaliaguet. Mean field games: the master equation and the mean field limit. Séminaire Laurent Schwartz — EDP et applications (2015-2016), Talk no. 17, 10 p. doi : 10.5802/slsedp.99. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.99/

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