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An Axiomatic Approach to the Concept of Interaction Among Players in Cooperative Games

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Author Info
Grabisch, M.
Roubens, M.

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Abstract

An axiomatization of the interactions between the palyers 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, the authors give an expression of the Banzhaf and Shapely interaction indices in terms of pseudo-Boolean functions.

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Publisher Info
Paper provided by UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie in its series Liege - Groupe d'Etude des Mathematiques du Management et de l'Economie with number 9818.

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Length: 23 pages
Date of creation: 1998
Date of revision:
Handle: RePEc:fth:gemame:9818

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Postal: UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie. 4000 Liege, BELGIQUE
Web page: http://www.sig.egss.ulg.ac.be/gemme/
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Related research
Keywords: GAME THEORY;

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Find related papers by 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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  1. René van den Brink & Gerard van der Laan, 2001. "A Class of Consistent Share Functions for Games in Coalition Structure," Tinbergen Institute Discussion Papers 01-044/1, Tinbergen Institute. [Downloadable!]
    Other versions:
  2. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985_v1, HAL. [Downloadable!]
  3. Gerard van der Laan & René van den Brink, 2002. "A Banzhaf share function for cooperative games in coalition structure," Theory and Decision, Springer, vol. 53(1), pages 61-86, August. [Downloadable!] (restricted)
    Other versions:
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