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

Mustapha Ridaoui (1) , Michel Grabisch (1) , Christophe Labreuche (2)

1 CES - Centre d'économie de la Sorbonne
2 Thales Research and Technology [Palaiseau]

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.

Mots clés: Banzhaf value; multicriteria decision aid; multichoice games; interaction

Domaines: Economies et finances; Mathématique discrète [cs.DM]

Mustapha Ridaoui, Michel Grabisch, Christophe Labreuche. An axiomatisation of the Banzhaf value and interaction index for multichoice games. Lecture Notes in Computer Sciences : International Conference on Modeling Decisions for Artificial Intelligence (MDAI), 2018. ⟨halshs-02381119⟩