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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2406.16409 |
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| _version_ | 1866917703355203584 |
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| author | Mermoud, Dylan Laplace Popoli, Pierre |
| author_facet | Mermoud, Dylan Laplace Popoli, Pierre |
| contents | In cooperative game theory, the social configurations of players are modeled by balanced collections. The Bondareva-Shapley theorem, perhaps the most fundamental theorem in cooperative game theory, characterizes the existence of solutions to the game that benefit everyone using balanced collections. Roughly speaking, if the trivial set system of all players is one of the most efficient balanced collections for the game, then the set of solutions from which each coalition benefits, the so-called core, is non-empty.
In this paper, we discuss some interactions between combinatorics and cooperative game theory that are still relatively unexplored. Indeed, the similarity between balanced collections and uniform hypergraphs seems to be a relevant point of view to obtain new properties on those collections through the theory of combinatorial species. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorics on Social Configurations Mermoud, Dylan Laplace Popoli, Pierre Computer Science and Game Theory Discrete Mathematics In cooperative game theory, the social configurations of players are modeled by balanced collections. The Bondareva-Shapley theorem, perhaps the most fundamental theorem in cooperative game theory, characterizes the existence of solutions to the game that benefit everyone using balanced collections. Roughly speaking, if the trivial set system of all players is one of the most efficient balanced collections for the game, then the set of solutions from which each coalition benefits, the so-called core, is non-empty. In this paper, we discuss some interactions between combinatorics and cooperative game theory that are still relatively unexplored. Indeed, the similarity between balanced collections and uniform hypergraphs seems to be a relevant point of view to obtain new properties on those collections through the theory of combinatorial species. |
| title | Combinatorics on Social Configurations |
| topic | Computer Science and Game Theory Discrete Mathematics |
| url | https://arxiv.org/abs/2406.16409 |