Linear Quadratic Nonzero Sum Differential Games with Asymmetric Information

This paper studies a linear quadratic nonzero sum differential game problem with asymmetric information. Compared with the existing literature, a distinct feature is that the information available to players is asymmetric. Nash equilibrium points are obtained for several classes of asymmetric information by stochastic maximum principle and technique of completion square. The systems of some Riccati equations and forward-backward stochastic filtering equations are introduced and the existence and uniqueness of the solutions are proved. Finally, the unique Nash equilibrium point for each class of asymmetric information is represented in a feedback form of the optimal filtering of the state, through the solutions of the Riccati equations.