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In this paper, the open-loop and closed-loop local and remote stochasticnonzero-sum game (LRSNG) problem is investigated. Different from previousworks, the stochastic nonzero-sum game problem under consideration isessentially a special class of two-person nonzero-sum game problem, in whichthe information sets accessed by the two players are inconsistent. Morespecifically, both the local player and the remote player are involved in thesystem dynamics, and the information sets obtained by the two players aredifferent, and each player is designed to minimize its own cost function. Forthe considered LRSNG problem, both the open-loop and closed-loop Nashequilibrium are derived. The contributions of this paper are given as follows.Firstly, the open-loop optimal Nash equilibrium is derived, which is determinedin terms of the solution to the forward and backward stochastic differenceequations (FBSDEs). Furthermore, by using the orthogonal decomposition methodand the completing square method, the feedback representation of the optimalNash equilibrium is derived for the first time. Finally, the effectiveness ofour results is verified by a numerical example.

Open-loop and Closed-loop Local and Remote Stochastic Nonzero-sum Game with Inconsistent Information Structure