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An axiomatic approach to the concept of interaction among players in cooperative games


  • Marc Roubens

    () (University of LiÉge, Institute of Mathematics, Grande Traverse 12, Sart-Tilman - B37, B-4000 LiÉge, Belgium)

  • Michel Grabisch

    () (Thomson-CSF, Central Research Laboratory, Domaine de Corbeville, F-91404 Orsay, France)


An axiomatization of the interaction between the players of any coalition is given. It is based on three axioms: linearity, dummy and symmetry. These interaction indices extend the Banzhaf and Shapley values when using in addition two equivalent recursive axioms. Lastly, we give an expression of the Banzhaf and Shapley interaction indices in terms of pseudo-Boolean functions.

Suggested Citation

  • Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
  • Handle: RePEc:spr:jogath:v:28:y:1999:i:4:p:547-565
    Note: Received: October 1997/revised version: October 1998

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    More about this item


    Cooperative games · interaction among players · Shapley values · Banzhaf values · coalition;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games


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