2026-04-17T02:42:11Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/3519542026-01-24T12:38:52Zcom_2072_1033col_2072_452950

urn:hdl:2117/351954 Weak null, necessary defender and necessary detractor players: characterizations of the Banzhaf and the Shapley bisemivalues Domènech Blázquez, Margarita Giménez Pradales, José Miguel Puente del Campo, María Albina Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs 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 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. This research project was partially supported by funds from the Spanish Ministry of Science and Innovation grant PID2019-104987GB-I00. Peer Reviewed Postprint (author's final draft) 2021-06-16 Article https://link.springer.com/article/10.1007%2Fs10479-021-04153-6 info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104987GB-I00/ES/JUEGOS DE VOTACION Y COOPERACION CON APLICACIONES A LAS REDES SOCIALES Y A LAS CIENCIAS POLITICAS/ Open Access Springer