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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.04012 |
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| _version_ | 1866912017274634240 |
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| author | Li, Wen Zou, Du Li, Deyi Feng, Yuqiang |
| author_facet | Li, Wen Zou, Du Li, Deyi Feng, Yuqiang |
| contents | The paper explores n-player multi-objective interval differential games, where the terminal payoff function and integral payoff function of players are both interval-vector-valued functions. Firstly, by leveraging the partial order relationship among interval vectors, we establish the concept of (weighted) open-loop Pareto-Nash equilibrium for multi-objective interval differential games and derive two theorems regarding the existence of such equilibria. Secondly, necessary conditions for open-loop Pareto-Nash equilibria in n-player interval differential games are derived through constructing Hamilton functions in an interval form and applying the Pontryagin maximum principle. Subsequently, sufficient conditions for their existence are provided by defining a maximization Hamilton function and utilizing its concavity. Finally, a two-player linear quadratic interval differential game is discussed along with a specific calculation method to determine its open-loop Pareto-Nash equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Open-loop Pareto-Nash equilibria in multi-objective interval differential games Li, Wen Zou, Du Li, Deyi Feng, Yuqiang Optimization and Control The paper explores n-player multi-objective interval differential games, where the terminal payoff function and integral payoff function of players are both interval-vector-valued functions. Firstly, by leveraging the partial order relationship among interval vectors, we establish the concept of (weighted) open-loop Pareto-Nash equilibrium for multi-objective interval differential games and derive two theorems regarding the existence of such equilibria. Secondly, necessary conditions for open-loop Pareto-Nash equilibria in n-player interval differential games are derived through constructing Hamilton functions in an interval form and applying the Pontryagin maximum principle. Subsequently, sufficient conditions for their existence are provided by defining a maximization Hamilton function and utilizing its concavity. Finally, a two-player linear quadratic interval differential game is discussed along with a specific calculation method to determine its open-loop Pareto-Nash equilibrium. |
| title | Open-loop Pareto-Nash equilibria in multi-objective interval differential games |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.04012 |