An axiomatisation of the Banzhaf value and interaction index for multichoice 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
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 a generalisa-tion 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 (search for similar items in EconPapers)
Date: 2018
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02381119
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Citations: View citations in EconPapers (2)

Published in Lecture Notes in Computer Sciences : International Conference on Modeling Decisions for Artificial Intelligence (MDAI), 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 multichoices games (2018)
Working Paper: An axiomatisation of the Banzhaf value and interaction index for multichoice games (2018)
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