In this paper, we investigate the mean field games of N agents who are weakly coupled via the empirical measures. The underlying dynamics of the representative agent is assumed to be a controlled nonlinear diffusion process with variable coefficients. We show that individual optimal strategies...

We prove that for any equilibrium of a (Bayesian) game, and any sequence of perturbations of that game, there exists a corresponding sequence of ex-ante ε-equilibria converging to the given equilibrium of the original game. We strengthen the conclusion to show that the approaching equilibria...

We study a one-dimensional stochastic motion of a tagged hard point moving among mechanically identical particles. At the initial moment the tagged particle is at rest separating two equal subvolumes L of gases at different in general thermal equilibrium states. Its further evolution is entirely...