On the Uniqueness of Nash Equilibria in Multiagent Matrix Games
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917812457439232 |
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| author | Bailey, James P. |
| author_facet | Bailey, James P. |
| contents | We provide a complete characterization for uniqueness of equilibria in unconstrained polymatrix games. We show that while uniqueness is natural for coordination and general polymatrix games, zero-sum games require that the dimension of the combined strategy space is even. Therefore, non-uniqueness is common in zero-sum polymatrix games. In addition, we study the impact of non-uniqueness on classical learning dynamics for multiagent systems and show that the classical methods still yield unique estimates even when there is not a unique equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Uniqueness of Nash Equilibria in Multiagent Matrix Games Bailey, James P. Computer Science and Game Theory We provide a complete characterization for uniqueness of equilibria in unconstrained polymatrix games. We show that while uniqueness is natural for coordination and general polymatrix games, zero-sum games require that the dimension of the combined strategy space is even. Therefore, non-uniqueness is common in zero-sum polymatrix games. In addition, we study the impact of non-uniqueness on classical learning dynamics for multiagent systems and show that the classical methods still yield unique estimates even when there is not a unique equilibrium. |
| title | On the Uniqueness of Nash Equilibria in Multiagent Matrix Games |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2410.16548 |