The Local and Remote Stochastic Nonzero-sum Game for Multiplicative Noise Systems

In this paper, the local and remote stochastic nonzero-sum game for a multiplicative noise system with inconsistent information structure is investigated, which multiplicative noise can cause nonlinear characteristics of linear systems, making it difficult to calculate the optimal estimator and the optimal linear feedback Nash equilibrium. For the local and remote stochastic nonzero-sum game, the local player and remote player can access different information, and each player is designed to minimize its own cost function. The contributions of this paper are summarized as follows. Firstly, the optimal open-loop Nash equilibrium is obtained in terms of the forward and backward stochastic difference equations (FBSDEs) by adopting the Pontryagin maximum principle. Secondly, a closed-loop Nash equilibrium to this local and remote stochastic nonzero-sum game for multiplicative noise system by using an orthogonal decomposition method is obtained. Finally, a simulation example is given to illustrate the validity of theoretical results.