Basins of Attraction in Two-Player Random Ordinal Potential Games
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912227621076992 |
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| author | Collevecchio, Andrea Mimun, Hlafo Alfie Quattropani, Matteo Scarsini, Marco |
| author_facet | Collevecchio, Andrea Mimun, Hlafo Alfie Quattropani, Matteo Scarsini, Marco |
| contents | We consider the class of two-person ordinal potential games where each player has the same number of actions $K$. Each game in this class admits at least one pure Nash equilibrium and the best-response dynamics converges to one of these pure Nash equilibria; which one depends on the starting point. So, each pure Nash equilibrium has a basin of attraction.
We pick uniformly at random one game from this class and we study the joint distribution of the sizes of the basins of attraction. We provide an asymptotic exact value for the expected basin of attraction of each pure Nash equilibrium, when the number of actions $K$ goes to infinity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_05460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Basins of Attraction in Two-Player Random Ordinal Potential Games Collevecchio, Andrea Mimun, Hlafo Alfie Quattropani, Matteo Scarsini, Marco Computer Science and Game Theory Theoretical Economics Probability Primary 91A14, 91A05. Secondary: 91A26, 60C05 We consider the class of two-person ordinal potential games where each player has the same number of actions $K$. Each game in this class admits at least one pure Nash equilibrium and the best-response dynamics converges to one of these pure Nash equilibria; which one depends on the starting point. So, each pure Nash equilibrium has a basin of attraction. We pick uniformly at random one game from this class and we study the joint distribution of the sizes of the basins of attraction. We provide an asymptotic exact value for the expected basin of attraction of each pure Nash equilibrium, when the number of actions $K$ goes to infinity. |
| title | Basins of Attraction in Two-Player Random Ordinal Potential Games |
| topic | Computer Science and Game Theory Theoretical Economics Probability Primary 91A14, 91A05. Secondary: 91A26, 60C05 |
| url | https://arxiv.org/abs/2407.05460 |