On Discrete-Time Approximations to Infinite Horizon Differential Games

Abstract

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 ǫ-Nash equilibrium for the continuous-time differential game. * Research supported by Spanish MCI under grants PID2019-104141GB-100 (AEI) (AEI/FEDER, UE) and VA169P20 (Junta de Castilla y Leon, ES) co-financed by FEDER funds (EU).