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

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Abstract.

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.

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Authors and Affiliations

  1. Thomson-CSF, Central Research Laboratory, Domaine de Corbeville, F-91404 Orsay, France (e-mail: michel.grabisch@lcr.thomson-csf.com), , , , , , FR

    Michel Grabisch

  2. University of Liège, Institute of Mathematics, Grande Traverse 12, Sart-Tilman – B37, B-4000 Liège, Belgium (e-mail: M.Roubens@ulg.ac.be), , , , , , BE

    Marc Roubens

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  1. Michel Grabisch
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  2. Marc Roubens
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Received: October 1997/revised version: October 1998

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Grabisch, M., Roubens, M. An axiomatic approach to the concept of interaction among players in cooperative games. Game Theory 28, 547–565 (1999). https://doi.org/10.1007/s001820050125

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  • DOI: https://doi.org/10.1007/s001820050125

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