Stochastic Linear-Quadratic Stackelberg Differential Game with Asymmetric Informational Uncertainties: Robust Optimization Approach
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917714876956672 |
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| author | Xiang, Na Shi, Jingtao |
| author_facet | Xiang, Na Shi, Jingtao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Linear-Quadratic Stackelberg Differential Game with Asymmetric Informational Uncertainties: Robust Optimization Approach Xiang, Na Shi, Jingtao Optimization and Control 93E20, 60H10, 91A15, 91A65 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. |
| title | Stochastic Linear-Quadratic Stackelberg Differential Game with Asymmetric Informational Uncertainties: Robust Optimization Approach |
| topic | Optimization and Control 93E20, 60H10, 91A15, 91A65 |
| url | https://arxiv.org/abs/2407.05728 |