Partial Information Differential Games for Mean-Field SDEs

TL;DR

This paper develops a stochastic maximum principle and verification theorem for Nash equilibria in mean-field differential games with partial information, and illustrates the results with a linear quadratic example.

Contribution

It introduces a new approach to characterize Nash equilibria in mean-field stochastic differential games with partial information using convex variations and Riccati equations.

Findings

Derived stochastic maximum principle for Nash equilibria.

Established verification theorem under additional assumptions.

Provided a linear quadratic example with explicit feedback form.

Abstract

This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum principle for Nash equilibrium points. Subsequently, under additional assumptions, verification theorem for Nash equilibrium points is also derived. Finally, as an application, a linear quadratic example is discussed. The unique Nash equilibrium point is represented in a feedback form of not only the optimal filtering but also expected value of the system state, throughout the solutions of the Riccati equations.