Linear-quadratic differential games for discrete-time stochastic systems with Markov jumps and multiplicative noise

In this paper, we consider the finite horizon nonzero-sum linear quadratic differential games for discrete-time stochastic systems with Markovian jumping parameters and multiplicative noise. A sufficient condition for the solutions of linear quadratic differential games is established from the solvability of four coupled generalized difference Riccati equations. Moreover, an iterative algorithm is employed to solve the four coupled equations and an illustrative example is also proposed to demonstrate the efficiency of the algorithm.