On Discrete-Time Approximations to Infinite Horizon Differential Games

12/06/2021

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by   Javier de Frutos, et al.

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In this paper we study a discrete-time semidiscretization 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 approximate the value function of the differential game. Furthermore, the discrete-time Nash equilibrium is an ϵ-Nash equilibrium for the continuous-time differential game.