Finite-horizon closed-loop Nash game for stochastic large-scale systems with multiple decision makers

The purpose of this paper is to investigate a finite-time horizon closed-loop Nash game for a class of stochastic systems. First, the condition necessary to attain Nash equilibrium is derived by means of stochastic maximum principle. When this principle is used, the existence conditions consist of cross-coupled forward-backward stochastic differential equations (CFBSDEs). Second, these results are then used to investigate closed-loop Nash games for a class of stochastic large-scale linear systems. Finally, simple examples are solved to show the validity of the proposed method.