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

TL;DR

This paper investigates stochastic nonzero-sum games with inconsistent information structures, deriving open-loop and closed-loop Nash equilibria and providing novel feedback representations, verified through numerical examples.

Contribution

It introduces the first feedback representation of Nash equilibria for such games, using orthogonal decomposition and completing square methods.

Findings

Derived open-loop Nash equilibrium via FBSDEs.

Established feedback Nash equilibrium with new methods.

Validated results with numerical example.

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 minimize 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.