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

Christophe Labreuche () and Michel Grabisch
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Christophe Labreuche: Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales) - THALES [France] - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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; Jeux coopératifs; jeux bi-coopératifs; indice de pouvoir; valeur de Shapley (search for similar items in EconPapers)
Date: 2006-03
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00113340v1
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Citations: View citations in EconPapers (4)

Published in 2006

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