The nonzero-sum games of discrete-time stochastic singular systems

In this paper, the problem of nonzero-sum games for discrete-time stochastic singular systems governed by Ito-type equation in finite-time horizon is discussed. Firstly, the problem is formulated, based on the problem, the particular case of nonzero-sum games - one-player case is discussed, then, the strategies for discrete-time stochastic singular systems are derived by extending the obtained result to two-player case. The existence of the strategies is presented by means of a set of cross-coupled Riccati algebraic equations and also the optimal control strategies are given.