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

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.
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Mustapha Ridaoui, Michel Grabisch, Christophe Labreuche. An axiomatisation of the Banzhaf value and interaction index for multichoices games. 2018. ⟨halshs-01814977⟩

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