Weak null, necessary defender and necessary detractor players: characterizations of the Banzhaf and the Shapley bisemivalues
We focus on bicooperative games, a variation of the classic cooperative games and, in particular, on the Banzhaf and the Shapley bisemivalues defined on these games. We consider three special classes of players: weak null, necessary defender and necessary detractor players. By introducing new proper...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/351954 |
| Acceso en línea: | https://hdl.handle.net/2117/351954 https://dx.doi.org/10.1007/s10479-021-04153-6 |
| Access Level: | acceso abierto |
| Palabra clave: | Cooperative games (Mathematics) Cooperative game Bicooperative game Banzhaf bisemivalue Shapley bisemivalue Jocs cooperatius (Matemàtica) Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs |
| Sumario: | We focus on bicooperative games, a variation of the classic cooperative games and, in particular, on the Banzhaf and the Shapley bisemivalues defined on these games. We consider three special classes of players: weak null, necessary defender and necessary detractor players. By introducing new properties related to this kind of players, we provide new axiomatic characterizations of the Banzhaf and the Shapley bisemivalues giving, in both cases, a set of independent properties that univocally determine them. We also provide a computational procedure to calculate the allocations given by the Shapley bisemivalue in terms of the generalized multilinear extension of the game. |
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