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...

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Detalles Bibliográficos
Autores: Domènech Blázquez, Margarita|||0000-0001-9237-7232, Giménez Pradales, José Miguel|||0000-0003-4754-194X, Puente del Campo, María Albina|||0000-0003-2732-9087
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
Descripción
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.