Linear-Quadratic Zero-Sum Stochastic Differential Game with Partial Observation
Optimization and Control
2025-10-29 v1
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.
Cite
@article{arxiv.2510.24493,
title = {Linear-Quadratic Zero-Sum Stochastic Differential Game with Partial Observation},
author = {Zhiyong Yu and Wanying Yue},
journal= {arXiv preprint arXiv:2510.24493},
year = {2025}
}