Mean field games have been introduced by J.-M. Lasry and P.-L. Lions as an effective model for very many competing rational agents. They are a system of Hamilton-Jacobi equations and Kolmogorov-Fokker-Planck equations. One of the challenges is the fact that these two types of equations have different “natural” notions of generalized solutions. We investigate dynamical mean field games in the small noise limit when the Hamilton-Jacobi equation of the system has a rapidly varying dependence on the state variable $x.$
This is joint work with Annalisa Cesaroni and Claudio Marchi.