The Convergence Problem in Mean Field Games with Neumann Boundary Conditions

In this article, we study the convergence of Nash equilibria in an N-player differential game towards the optimal strategies in the mean field games when the dynamic of the generic player includes a reflection process which guarantees the invariance of the state space \Omega . The well-posedness of the master equation allows us to use its solution U in order to construct finite-dimensional projections uNi, which will satisfy | uNi - vNi| \rightarrow 0 forN\rightarrow +\infty almost surely, where (vNi)iis the solution of the Nash system.