  This paper is concerned with a leader-follower stochastic differential game
with asymmetric information, where the information available to the follower is
based on some sub-$\sigma$-algebra of that available to the leader. Such kind
of game problem has wide applications in finance, economics and management
engineering such as newsvendor problems, cooperative advertising and pricing
problems. Stochastic maximum principles and verification theorems with partial
information are obtained, to represent the Stackelberg equilibrium. As
applications, a linear-quadratic leader-follower stochastic differential game
with asymmetric information is studied. It is shown that the open-loop
Stackelberg equilibrium admits a state feedback representation if some system
of Riccati equations is solvable.
