The equilibrium-value convergence for the multiple-partners game
We study the assignment game (Shapley and Shubik, 1972) and its generalization of the multiple-partners game (Sotomayor, 1992), the simplest many-to-many extension. Our main result is that the Shapley value of a replicated multiple-partners game converges to a competitive equilibrium payoff when the...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:300002 |
| Acesso em linha: | https://ddd.uab.cat/record/300002 https://dx.doi.org/urn:doi:10.1016/j.jet.2024.105870 |
| Access Level: | acceso abierto |
| Palavra-chave: | Assignment game Shapley value Replica Semivalues |
| Resumo: | We study the assignment game (Shapley and Shubik, 1972) and its generalization of the multiple-partners game (Sotomayor, 1992), the simplest many-to-many extension. Our main result is that the Shapley value of a replicated multiple-partners game converges to a competitive equilibrium payoff when the number of replicas tends to infinity. The result also holds for a large subclass of semivalues since we prove that they converge to the same value as the replica becomes large. Furthermore, in supermodular and monotonic assignment games, the asymptotic Shapley value coincides with the mean stable imputation. The proof of our theorem relies on Hall's theorem. |
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