Por Marco Masoero (Université Paris-Dauphine).

Abstract: We look at the long time behavior of potential Mean field games (briefly MFG) using some standard tools from weak KAM theory. We first show that the time-dependent minimization problem converges to an ergodic constant -\lambda, then we provide a class of examples where the value of the stationary MFG minimization problem is strictly greater than -\lambda. This will imply that the trajectories of the time-dependent MFG system do  not converge to static equilibria.