A New Feedback Form of Open-Loop Stackelberg Strategy in a General Linear-Quadratic Differential Game
In this paper, we consider a general form of linear-quadratic Stackelberg deterministic differential game model, which consists of one leader and one follower. Each of their utility functions includes all possible squared terms, cross terms and single terms of states and controls of the two players,...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
2023
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| Online Access: | http://purl.org/au-research/grants/arc/DP190103361 http://hdl.handle.net/20.500.11937/91972 |
| _version_ | 1848765609553166336 |
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| author | Li, Y. Teo, Kok Lay Zhang, S. |
| author_facet | Li, Y. Teo, Kok Lay Zhang, S. |
| author_sort | Li, Y. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a general form of linear-quadratic Stackelberg deterministic differential game model, which consists of one leader and one follower. Each of their utility functions includes all possible squared terms, cross terms and single terms of states and controls of the two players, and constant terms. The time-consistent state feedback form of Stackelberg equilibrium strategy is obtained. Its explicit expression is in terms of the solutions of three decoupled symmetric Riccati differential equations. These decoupled symmetric Riccati differential equations are independent of the state and can be solved backward in time one by one. The proposed model and theory are applied to some classical Stackelberg games |
| first_indexed | 2025-11-14T11:37:58Z |
| format | Journal Article |
| id | curtin-20.500.11937-91972 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:37:58Z |
| publishDate | 2023 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-919722024-10-08T04:31:59Z A New Feedback Form of Open-Loop Stackelberg Strategy in a General Linear-Quadratic Differential Game Li, Y. Teo, Kok Lay Zhang, S. In this paper, we consider a general form of linear-quadratic Stackelberg deterministic differential game model, which consists of one leader and one follower. Each of their utility functions includes all possible squared terms, cross terms and single terms of states and controls of the two players, and constant terms. The time-consistent state feedback form of Stackelberg equilibrium strategy is obtained. Its explicit expression is in terms of the solutions of three decoupled symmetric Riccati differential equations. These decoupled symmetric Riccati differential equations are independent of the state and can be solved backward in time one by one. The proposed model and theory are applied to some classical Stackelberg games 2023 Journal Article http://hdl.handle.net/20.500.11937/91972 10.3934/jimo.2022105 http://purl.org/au-research/grants/arc/DP190103361 fulltext |
| spellingShingle | Li, Y. Teo, Kok Lay Zhang, S. A New Feedback Form of Open-Loop Stackelberg Strategy in a General Linear-Quadratic Differential Game |
| title | A New Feedback Form of Open-Loop Stackelberg Strategy in a General Linear-Quadratic Differential Game |
| title_full | A New Feedback Form of Open-Loop Stackelberg Strategy in a General Linear-Quadratic Differential Game |
| title_fullStr | A New Feedback Form of Open-Loop Stackelberg Strategy in a General Linear-Quadratic Differential Game |
| title_full_unstemmed | A New Feedback Form of Open-Loop Stackelberg Strategy in a General Linear-Quadratic Differential Game |
| title_short | A New Feedback Form of Open-Loop Stackelberg Strategy in a General Linear-Quadratic Differential Game |
| title_sort | new feedback form of open-loop stackelberg strategy in a general linear-quadratic differential game |
| url | http://purl.org/au-research/grants/arc/DP190103361 http://hdl.handle.net/20.500.11937/91972 |