# The master equation and the convergence problem in mean-field games

Monday, October 26, 2015 -

4:30pm to 5:30pm

We discuss the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, called the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called ``master equation", a kind of second order partial differential equation stated on the space of probability measures. Our first main result is the well-posedness of the master equation. To do so, we first show the existence and uniqueness of a solution to the ``mean field game system with common noise", which consists in a coupled system made of a backward stochastic Hamilton-Jacobi equation and a forward stochastic Kolmogorov equation and which plays the role of characteristics for the master equation. Our second main result is the convergence, in average, of the solution of the Nash system and a propagation of chaos property for the associated ``optimal trajectories". Joint work with J.F. Chassagneux and D. Crisan; and P. Cardaliaguet, J.M. Lasry and P.L. Lions.

Speaker:

FranÃ§ois Delarue

UniversitÃ© Nice-Sophia Antipolis

Event Location:

Fine Hall 214