A categorical representation of games
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915155891191808 |
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| author | Tohmé, Fernando Viglizzo, Ignacio |
| author_facet | Tohmé, Fernando Viglizzo, Ignacio |
| contents | Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players $\mathbf{Gam}_I$ is built from this representation, and a more general category $\mathbf{Gam}$ is defined with games having different sets of players, both being complete and cocomplete. The notion of Nash equilibrium can be generalized in this context. We then introduce two subcategories of $\mathbf{Gam}$, $\mathbf{NE}$ and $\mathbf{Gam}^{NE}$ in which the morphisms are equilibria-preserving. We illustrate the expressivity and usefulness of this framework with some examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15981 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A categorical representation of games Tohmé, Fernando Viglizzo, Ignacio Category Theory 18A35, 91A35 Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players $\mathbf{Gam}_I$ is built from this representation, and a more general category $\mathbf{Gam}$ is defined with games having different sets of players, both being complete and cocomplete. The notion of Nash equilibrium can be generalized in this context. We then introduce two subcategories of $\mathbf{Gam}$, $\mathbf{NE}$ and $\mathbf{Gam}^{NE}$ in which the morphisms are equilibria-preserving. We illustrate the expressivity and usefulness of this framework with some examples. |
| title | A categorical representation of games |
| topic | Category Theory 18A35, 91A35 |
| url | https://arxiv.org/abs/2309.15981 |