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In this article we study the convergence of the Nash Equilibria in a N-playerdifferential game towards the optimal strategies in the Mean Field Games, whenthe dynamic of the generic player includes a reflection process whichguarantees the invariance of the state space. The well-posedness of the MasterEquation allows us to use its solution U in order to construct finitedimensional projections, which will converge, in some suitable spaces, to thesolution of the Nash system.

The Convergence Problem in Mean Field Games with Neumann Boundary Conditions