A Linear Quadratic Stochastic Stackelberg Differential Game with Time Delay

TL;DR

This paper studies a complex linear quadratic stochastic Stackelberg differential game with both state and control delays affecting the system dynamics and diffusion, providing a feedback strategy derivation through Riccati equations.

Contribution

It introduces a novel approach using Pseudo-Riccati and matrix equations to derive feedback strategies in delayed stochastic Stackelberg games.

Findings

Derived state feedback strategies for delayed stochastic Stackelberg games.

Established conditions for the existence of solutions using Riccati equations.

Illustrated theoretical results with practical examples.

Abstract

This paper is concerned with a linear quadratic stochastic Stackelberg differential game with time delay. The model is general, in which the state delay and the control delay both appear in the state equation, moreover, they both enter into the diffusion term. By introducing two Pseudo-Riccati equations and a special matrix equation, the state feedback representation of the open-loop Stackelberg strategy is derived, under some assumptions. Finally, two examples are given to illustrate the applications of the theoretical results.