Finite horizon linear quadratic dynamic games for discrete-time stochastic systems with NN-players

In this paper, dynamic games for a class of finite horizon linear stochastic system governed by Itô’s difference equation are investigated. Particularly, both Pareto and Nash strategies are discussed. After defining the equilibrium condition, sufficient conditions for the existence of the strategy sets are obtained, which are associated with the solvability of the corresponding generalized difference Riccati equations (GDREs). Furthermore, an iterative algorithm is proposed to solve the related GDREs and a simple numerical example is given to show the reliability and usefulness of the considerable results.