Linear-quadratic Stochastic Stackelberg Differential Games with Affine Constraints
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916543284117504 |
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| author | Gou, Zhun Huang, Nan-Jing Long, Xian-Jun Kang, Jian-Hao |
| author_facet | Gou, Zhun Huang, Nan-Jing Long, Xian-Jun Kang, Jian-Hao |
| contents | This paper investigates the non-zero-sum linear-quadratic stochastic Stackelberg differential games with affine constraints, which depend on both the follower's response and the leader's strategy. With the help of the stochastic Riccati equations and the Lagrangian duality theory, the feedback expressions of optimal strategies of the follower and the leader are obtained and the dual problem of the leader's problem is established. Under the Slater condition, the equivalence is proved between the solutions to the dual problem and the leader's problem, and the KKT condition is also provided for solving the dual problem. Then, the feedback Stackelberg equilibrium is provided for the linear-quadratic stochastic Stackelberg differential games with affine constraints, and a new positive definite condition is proposed for ensuring the uniqueness of solutions to the dual problem. Finally, two non-degenerate examples with indefinite coefficients are provided to illustrate and to support our main results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18802 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear-quadratic Stochastic Stackelberg Differential Games with Affine Constraints Gou, Zhun Huang, Nan-Jing Long, Xian-Jun Kang, Jian-Hao Optimization and Control This paper investigates the non-zero-sum linear-quadratic stochastic Stackelberg differential games with affine constraints, which depend on both the follower's response and the leader's strategy. With the help of the stochastic Riccati equations and the Lagrangian duality theory, the feedback expressions of optimal strategies of the follower and the leader are obtained and the dual problem of the leader's problem is established. Under the Slater condition, the equivalence is proved between the solutions to the dual problem and the leader's problem, and the KKT condition is also provided for solving the dual problem. Then, the feedback Stackelberg equilibrium is provided for the linear-quadratic stochastic Stackelberg differential games with affine constraints, and a new positive definite condition is proposed for ensuring the uniqueness of solutions to the dual problem. Finally, two non-degenerate examples with indefinite coefficients are provided to illustrate and to support our main results. |
| title | Linear-quadratic Stochastic Stackelberg Differential Games with Affine Constraints |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.18802 |