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arXiv · 2407.05728

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

Na Xiang·Jingtao Shi
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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.

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Na Xiang, Jingtao Shi. 2024-07-08. Stochastic Linear-Quadratic Stackelberg Differential Game with Asymmetric Informational Uncertainties: Robust Optimization Approach. https://arxiv.org/abs/2407.05728

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