Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

TL;DR

This paper studies a stochastic linear quadratic Stackelberg differential game with overlapping information, deriving optimal controls using stochastic maximum principle, filtering, and Riccati equations, with applications to principal-agent problems.

Contribution

It introduces a new Riccati system for state estimate feedback in Stackelberg games with overlapping information, advancing solution methods for such complex dynamic games.

Findings

Derived explicit optimal controls for leader and follower.

Established a new Riccati equation system for state estimation.

Applied the framework to a principal-agent problem.

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.