In this chapter, we discuss a leader-follower (also called Stackelberg) stochastic differential game with asymmetric information. Here the word “asymmetric” means that the available information of the follower is some sub- σ -algebra of that available to the leader, though they play as different roles in the classical literatures. Stackelberg equilibrium is represented by the stochastic versions of Pontryagin’s maximum principle and verification theorem with partial information. A linear-quadratic (LQ) leader-follower stochastic differential game with asymmetric information is studied as applications. If some system of Riccati equations is solvable, the Stackelberg equilibrium admits a state feedback representation.
Part of the book: Game Theory