A Problem of Calculus of Variations and Game Theory
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866915002503397376 |
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| author | Luo, Grace Boyer, Christopher Penmetsa, Siddharth |
| author_facet | Luo, Grace Boyer, Christopher Penmetsa, Siddharth |
| contents | In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented, followed by computer analysis as well as polynomial approximation. Nash equilibrium strategies are determined through algebraic manipulation and linear programming. Lastly, a variation of the game is also investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Problem of Calculus of Variations and Game Theory Luo, Grace Boyer, Christopher Penmetsa, Siddharth Optimization and Control 49M05 (primary) 90C05, 91A05 (secondary) In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented, followed by computer analysis as well as polynomial approximation. Nash equilibrium strategies are determined through algebraic manipulation and linear programming. Lastly, a variation of the game is also investigated. |
| title | A Problem of Calculus of Variations and Game Theory |
| topic | Optimization and Control 49M05 (primary) 90C05, 91A05 (secondary) |
| url | https://arxiv.org/abs/2411.00791 |