Open-loop and closed-loop local and remote stochastic nonzero-sum game with inconsistent information structure

Abstract

In this paper, the open-loop and closed-loop local and remote stochastic nonzero-sum game (LRSNG) problem is investigated. Different from previous works, the stochastic nonzero-sum game problem under consideration is essentially a special class of two-person nonzero-sum game problem, in which the information sets accessed by the two players are inconsistent. More specifically, both the local player and the remote player are involved in the system dynamics, and the information sets obtained by the two players are different, and each player is designed to minimise its own cost function. For the considered LRSNG problem, both the open-loop and closed-loop Nash equilibrium are derived. The contributions of this paper are given as follows. Firstly, the open-loop optimal Nash equilibrium is derived, which is determined in terms of the solution to the forward and backward stochastic difference equations (FBSDEs). Furthermore, by using the orthogonal decomposition method and the completing square method, the feedback representation of the optimal Nash equilibrium is derived for the first time. Finally, the effectiveness of our results is verified by a numerical example.

Keywords:

• Discrete-time stochastic nonzero-sum game
• inconsistent information structure
• open-loop and closed-loop Nash equilibrium
• maximum principle

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by China Postdoctoral Science Foundation [2019M652324, 2021T140354], National Natural Science Foundation of China [61903210], Natural Science Foundation of Shandong Province [ZR2019BF002], Qingdao Postdoctoral Application Research Project, Major Basic Research of Natural Science Foundation of Shandong Province [ZR2021ZD14].