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An axiomatic approach to the concept of interaction among players in cooperative games |
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| Authors: | Michel Grabisch Marc Roubens |
| Affiliation: | (1) Thomson-CSF, Central Research Laboratory, Domaine de Corbeville, F-91404 Orsay, France (e-mail: michel.grabisch@lcr.thomson-csf.com), FR;(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 |
| 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. Received: October 1997/revised version: October 1998 |
| Keywords: | : Cooperative games interaction among players Shapley values Banzhaf values coalition |
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