Maximum Principle for Partial Observed Zero-Sum Stochastic Differential Game of Mean-Field SDEs

TL;DR

This paper develops maximum principles for a two-player zero-sum stochastic differential game with mean-field dynamics under partial observation, extending control theory to complex stochastic systems.

Contribution

It introduces maximum principles for partial observed mean-field stochastic differential games and analyzes linear quadratic cases with saddle point characterizations.

Findings

Established maximum principles for partial observed mean-field stochastic games.

Derived existence and dual characterization of saddle points in linear quadratic cases.

Extended stochastic control theory to complex partial observation scenarios.

Abstract

In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients, the maximum principles for optimal open-loop control in a strong sense as well as a weak one are established by the associated optimal control theory in Tang and Meng (2016). To illustrate the general results, a class of linear quadratic stochastic differential game problem is discussed and the existence and dual characterization for the partially observed open-loop saddle are obtained.