Stochastic Linear-Quadratic Stackelberg Differential Game with Asymmetric Informational Uncertainties: Robust Optimization Approach

TL;DR

This paper develops a robust optimization framework for a stochastic Stackelberg differential game with asymmetric uncertainties, providing explicit feedback strategies through Riccati equations.

Contribution

It introduces a novel approach to handle asymmetric informational uncertainties in stochastic Stackelberg games using robust optimization and decoupling techniques.

Findings

Explicit state feedback representation of equilibrium strategies.

Solution of min-max and max-min control problems via Riccati equations.

Application to asymmetric informational uncertainties in stochastic differential games.

Abstract

This paper is concerned with a two-person zero-sum indefinite stochastic linear-quadratic Stackelberg differential game with asymmetric informational uncertainties, where both the leader and follower face different and unknown disturbances. We take a robust optimization approach and soft-constraint analysis, a min-max stochastic linear-quadratic optimal control problem is solved by the follower firstly. Then, the leader deal with a max-min stochastic linear-quadratic optimal control problem of forward-backward stochastic differential equations in an augmented space. State feedback representation of the robust Stackelberg equilibrium is given in a more explicit form by decoupling technique, via some Riccati equations.