The Convergence Problem in Mean Field Games with Neumann Boundary Conditions
Michele Ricciardi · SIAM Journal on Mathematical Analysis · 2023
Abstract. In this article, we study the convergence of Nash equilibria in an [Formula: see text]-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 [Formula: see text]. The well-posedness of the master equation allows us to use its solution [Formula: see text] in order to construct finite-dimensional projections [Formula: see text], which will satisfy [Formula: see text] for [Formula: see text] almost surely, where [Formula: see text] is the solution of the Nash system.