Leader-Follower Stochastic Differential Game with Asymmetric Information and Applications

TL;DR

This paper studies a leader-follower stochastic differential game with asymmetric information, deriving equilibrium conditions and applying them to linear-quadratic cases with practical applications in finance and management.

Contribution

It develops stochastic maximum principles and verification theorems for partial information games, providing a framework for representing Stackelberg equilibria in such settings.

Findings

Derived stochastic maximum principles for asymmetric information games.

Established conditions for state feedback representation of equilibria.

Applied results to linear-quadratic models with solvable Riccati equations.

Abstract

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.