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An Axiomatisation of the Banzhaf Value and Interaction Index for Multichoice Games

  • Mustapha Ridaoui
  • Michel Grabisch
  • Christophe Labreuche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11144)

Abstract

We provide an axiomatisation of the Banzhaf value (or power index) and the Banzhaf interaction index for multichoice games, which are a 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 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mustapha Ridaoui
    • 1
  • Michel Grabisch
    • 1
  • Christophe Labreuche
    • 2
  1. 1.Paris School of EconomicsUniversité Paris I - Panthéon-SorbonneParisFrance
  2. 2.Thales Research and TechnologyPalaiseauFrance

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