Differential games for time-varying discrete-time stochastic systems with multiplicative noise

In this paper, we consider the differential games for time-varying discrete-time stochastic systems with multiplicative noise in finite-time horizon. We give the optimal strategies (Nash equilibrium strategies) and the optimal cost values for the stochastic differential games. It is presented that the stochastic differential games are associated with four coupled generalized algebraic Riccati equations. Furthermore, an iterative algorithm is proposed to solve the four coupled equations and an example is presented to illustrate the effectiveness of the iterative algorithm.