Weak null, necessary defender and necessary detractor players: characterizations of the Banzhaf and the Shapley bisemivalues

Margarita Domènech (), José Miguel Giménez () and María Albina Puente ()
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Margarita Domènech: Technical University of Catalonia
José Miguel Giménez: Technical University of Catalonia
María Albina Puente: Technical University of Catalonia

Annals of Operations Research, 2022, vol. 318, issue 2, No 9, 889-910

Abstract: Abstract 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.

Keywords: Cooperative game; Bicooperative game; Banzhaf bisemivalue; Shapley bisemivalue; 91A12 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-021-04153-6

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