An axiomatisation of the Banzhaf value and interaction index for multichoices games

Mustapha Ridaoui (), Michel Grabisch and Christophe Labreuche ()
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Mustapha Ridaoui: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Christophe Labreuche: Thales Research and Technology [Palaiseau] - THALES [France]

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Abstract: We provide an axiomatisation of the Banzhaf value (or power index) and the Banzhaf interaction index for multichoice games, which are generalisation of cooperative games with several levels of participation. Multichoice games can model any aggregation model in multicriteria decision making, provided the attributes take a finite number of values. Our axiomatisation uses standard axioms of the Banzhaf value for classical games (linearity, null axiom, symmetry), an invariance axiom specific to the multichoice context, and a generalisation of the 2-efficiency axiom, characteristic of the Banzhaf value.

Keywords: Banzhaf value; multicriteria decision aid; multichoice games; interaction; valeur de Banzhaf; décision multicritère; jeu multichoix (search for similar items in EconPapers)
Date: 2018-03
New Economics Papers: this item is included in nep-bec and nep-gth
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01814977v1
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Published in 2018

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Related works:
Working Paper: An axiomatisation of the Banzhaf value and interaction index for multichoices games (2018)
Working Paper: An axiomatisation of the Banzhaf value and interaction index for multichoice games (2018)
Working Paper: An axiomatisation of the Banzhaf value and interaction index for multichoice games (2018)
Working Paper: An axiomatisation of the Banzhaf value and interaction index for multichoice games (2018)
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