This talk is devoted to the convergence problem of the Nash Equilibria in an N-player differential game towards the optimal strategies in the Mean-Field Games framework. The novelty here is that the dynamic of the generic player includes a reflection process which guarantees the invariance of the state space Ω. This implies that the MFG system presents Neumann boundary conditions for the value function u and the density of the population m. The first part of the talk is devoted to the study of the well-posedness of the Master Equation, essential tool in order to study the convergence problem. The reflection process in the N-players game leads to two Neumann conditions in the Master Equation formulation. In the second part we analyse the convergence problem, borrowing and readapting the ideas from the periodic case, studied by Cardaliaguet, Delarue, Lasry, Lions. The results can also be generalized in the case of Dirichlet boundary conditions.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
