On Characterizations of Potential and Ordinal Potential Games
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916241653891072 |
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| author | Arefizadeh, Sina Nedich, Angelia Dasarathy, Gautam |
| author_facet | Arefizadeh, Sina Nedich, Angelia Dasarathy, Gautam |
| contents | This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with multi-dimensional action spaces, which require differentiable cost functions. Then, we provide a necessary and sufficient conditions for a game to have a potential function by investigating the structure of a potential function in terms of the players' cost differences, as opposed to differentials. This condition provides a systematic way for construction of a potential function, which is applied to network congestion games, as an example. Finally, we provide some sufficient conditions for a game to be ordinal potential and generalized ordinal potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Characterizations of Potential and Ordinal Potential Games Arefizadeh, Sina Nedich, Angelia Dasarathy, Gautam Computer Science and Game Theory Optimization and Control This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with multi-dimensional action spaces, which require differentiable cost functions. Then, we provide a necessary and sufficient conditions for a game to have a potential function by investigating the structure of a potential function in terms of the players' cost differences, as opposed to differentials. This condition provides a systematic way for construction of a potential function, which is applied to network congestion games, as an example. Finally, we provide some sufficient conditions for a game to be ordinal potential and generalized ordinal potential. |
| title | On Characterizations of Potential and Ordinal Potential Games |
| topic | Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2405.06253 |