*Pierre Cardaliaguet (Paris-Dauphine)*

We will discuss 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. We describe the limit problem in terms of the so-called “master equation”, a kind of transport equation stated on the space of probability measures. This is a just work with F. Delarue, J.-M. Lasry and P.L. Lions.