Mean-Field Partial Information Non-zero Sum Stochastic Differential Games

Abstract

In this paper, we study a general mean-field partial information non-zero sum stochastic differential game, in which the dynamic of state is described by a stochastic differential equation (SDE) depending on the distribution of the state and the control domain of each player can be non-convex. Moreover, the control variables of both players can enter the diffusion coefficients of the state equation. We establish a necessary condition in the form of Pontryagin’s maximum principle for optimality. Then a verification theorem is obtained for optimal control when the control domain is convex. As an application, our results are applied to studying linear–quadratic (LQ) mean-field game in the type of scalar interaction.