Multiplayer General Lotto game
Fuente:
arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916988664676352 |
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| author | Liu, Yan Ni, Bonan Shen, Weiran Wang, Zihe Zhang, Jie |
| author_facet | Liu, Yan Ni, Bonan Shen, Weiran Wang, Zihe Zhang, Jie |
| contents | In this paper, we investigate the multiplayer General Lotto game across multiple battlefields, a significant variant of the Colonel Blotto game. In this version, each player employs a probability distribution for resource allocation, ensuring that their expected expenditure does not exceed their budget. We first establish the existence of the Nash equilibrium in a general setting, where players' budgets are asymmetric and the values of the battlefields are heterogeneous and asymmetric among players. Next, we provide a detailed characterization of the Nash equilibrium for multiple players on a single battlefield. In this characterization, we observe that the upper endpoints of the supports of players' equilibrium strategies coincide, and that the minimum value of a player's support above zero inversely correlates with his budget. We demonstrate the uniqueness of Nash equilibrium over a single battlefield in some scenarios. In the multi-battlefield setting, we prove that there is an upper bound on the average number of battlefields each player participates in. Additionally, we provide an example demonstrating the non-uniqueness of the Nash equilibrium in the context of multiple battlefields with multiple players. Finally, we present a solution for the Nash equilibrium in a symmetric case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14613 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplayer General Lotto game Liu, Yan Ni, Bonan Shen, Weiran Wang, Zihe Zhang, Jie Computer Science and Game Theory In this paper, we investigate the multiplayer General Lotto game across multiple battlefields, a significant variant of the Colonel Blotto game. In this version, each player employs a probability distribution for resource allocation, ensuring that their expected expenditure does not exceed their budget. We first establish the existence of the Nash equilibrium in a general setting, where players' budgets are asymmetric and the values of the battlefields are heterogeneous and asymmetric among players. Next, we provide a detailed characterization of the Nash equilibrium for multiple players on a single battlefield. In this characterization, we observe that the upper endpoints of the supports of players' equilibrium strategies coincide, and that the minimum value of a player's support above zero inversely correlates with his budget. We demonstrate the uniqueness of Nash equilibrium over a single battlefield in some scenarios. In the multi-battlefield setting, we prove that there is an upper bound on the average number of battlefields each player participates in. Additionally, we provide an example demonstrating the non-uniqueness of the Nash equilibrium in the context of multiple battlefields with multiple players. Finally, we present a solution for the Nash equilibrium in a symmetric case. |
| title | Multiplayer General Lotto game |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2401.14613 |