Linear-Quadratic Zero-Sum Stochastic Differential Game with Partial Observation

TL;DR

This paper develops a framework for solving linear-quadratic zero-sum stochastic differential games with partial observation, introducing feedback laws and applying them to a duopoly competition scenario.

Contribution

It introduces explicit and implicit feedback laws for LQ zero-sum stochastic differential games under partial observation, utilizing CMF-SDEs and separation principles.

Findings

Constructed saddle point feedback laws for the game

Applied the theoretical framework to a duopoly competition model

Demonstrated the effectiveness of the approach in partial observation settings

Abstract

This paper is concerned with a kind of linear-quadratic (LQ, for short) two-person zero-sum stochastic differential game problems with partial observation. We propose the notions of explicit and implicit feedback laws under partial observation. With the help of a class of conditional mean-field stochastic differential equations (CMF-SDEs, for short), the separation principle, filtering techniques, and the method of completion of squares, we construct a saddle point in the form of feedback laws for the two players. Finally, the theoretical results are applied to investigate a duopoly competition problem with partial observation.