Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

Abstract

This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term "overlapping" means that there are common part between the follower's and the leader's information, while they have no inclusion relation. Optimal controls of the follower and the leader are obtained by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to represent the state estimate feedback of the Stackelberg equilibrium strategy. A special solvable case is then studied and is applied to the continuous-time principal-agent problem.