Axiomatization of the Shapley value and power index for bi-cooperative games

Christophe Labreuche () and Michel Grabisch
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Christophe Labreuche: Thales Research & Technology

Cahiers de la Maison des Sciences Economiques from Université Panthéon-Sorbonne (Paris 1)

Abstract: Bi-cooperative games have been introduced by Bilbao as a generalization of classical cooperative games, where each player can participate positively to the game (defender), negatively (defeater), or do not participate (abstentionist). In a voting situation (simple games), they coincide with ternary voting game of Felsenthal and Mochover, where each voter can vote in favor, against or abstain. In this paper, we propose a definition of value or solution concept for bi-cooperative games, close to the Shapley value, and we give an interpretation of this value in the framework of (ternary) simple games, in the spirit of Shapley-Shubik, using the notion of swing. Lastly, we compare our definition with the one of Felsenthal and Machover, based on the notion of ternary roll-call, and the Shapley value of multi-choice games proposed by Hsiao and Ragahavan

Keywords: Cooperative game theory; bi-cooperative games; power index; Shapley value (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2006-03
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Related works:
Working Paper: Axiomatisation of the Shapley value and power index for bi-cooperative games (2006)
Working Paper: Axiomatisation of the Shapley value and power index for bi-cooperative games (2006)
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