A Verification Theorem for Stackelberg Stochastic Differential Games in Feedback Information Pattern

TL;DR

This paper establishes a verification theorem for feedback Stackelberg stochastic differential games using PDEs and applies it to linear quadratic cases with Riccati equations, providing analytical and numerical solutions.

Contribution

It introduces a verification theorem for feedback Stackelberg equilibria in stochastic differential games using PDEs and Riccati equations.

Findings

Verification theorem based on PDEs for feedback Stackelberg equilibrium

Analytical solutions for Riccati equations in special cases

Numerical solutions for Riccati equations in linear quadratic games

Abstract

This paper is concerned with a Stackelberg stochastic differential game on a finite horizon in feedback information pattern. A system of parabolic partial differential equations is obtained at the level of Hamiltonian to give the verification theorem of the feedback Stackelberg equilibrium. As an example, a linear quadratic Stackelberg stochastic differential game is investigated. Riccati equations are introduced to express the feedback Stackelberg equilibrium, analytical and numerical solutions to these Riccati equations are discussed in some special cases.