Zero-sum stochastic linear-quadratic Stackelberg differential games of Markovian regime-switching system

Abstract

This paper investigates a zero-sum stochastic linear-quadratic (SLQ, for short) Stackelberg differential game problem, where the coefficients of the state equation and the weighting matrices in the performance functional are regulated by a Markov chain. By utilizing the findings in \citet{Zhang.X.2021_ILQM}, we directly present the feedback representation to the rational reaction of the follower. For the leader's problem, we derive the optimality system through the variational method and study its unique solvability from the Hilbert space point of view. We construct the explicit optimal control for the leader based on the solution to coupled differential Riccati equations (CDREs, for short) and obtain the solvability of CDREs under the one-dimensional framework. Finally, we provide two concrete examples to illustrate the results developed in this paper.