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In this paper we study a discrete-time discretization of an infinite time horizon noncooperative N-player differential game. We prove that as the discretization time step approaches zero the discrete-time value function approximates the value function of the differential game. Furthermore, the discrete-time Nash equilibrium is an ϵ-Nash equilibrium for the continuous-time differential game. We present some numerical experiments and discuss to what extent the hypotheses are general enough to cover some common applications.
(with V. Gatón and J. Novo)