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

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.
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Submitted on : Monday, November 13, 2006 - 9:49:54 AM
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Christophe Labreuche, Michel Grabisch. Axiomatisation of the Shapley value and power index for bi-cooperative games. 2006. ⟨halshs-00113340⟩

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