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Associated consistency and Shapley value


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  • Gérard Hamiache

    (CERESUR, Centre d'Études et de Recherches Économiques et Sociales de l'Université de La Réunion and GREQAM, Groupement de Recherche en Économie Quantitative d'Aix-Marseille. Accepted September 2001)

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    In this work, a new axiomatization of the Shapley is presented. An associated game is constructed. We define a sequence of games, when the term of order n, in this sequence, is the associated game of the term of order (n-1). We show that the sequence converges and that the limit game is inessential. The solution is obtained using the inessential game axiom, the associated consistency axiom and the continuity axiom. As a by-product, we note that neither the additivity nor the efficiency axioms are needed.

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 30 (2001)
    Issue (Month): 2 ()
    Pages: 279-289

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    Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:279-289

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    Keywords: Shapley value · associated game · consistency.;


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    Cited by:
    1. Kongo, T. & Funaki, Y. & Tijs, S.H., 2007. "New Axiomatizations and an Implementation of the Shapley Value," Discussion Paper 2007-90, Tilburg University, Center for Economic Research.
    2. Theo Driessen, 2010. "Associated consistency and values for TU games," International Journal of Game Theory, Springer, vol. 39(3), pages 467-482, July.
    3. Gérard Hamiache, 2012. "A Matrix Approach to TU Games with Coalition and Communication Structures," Social Choice and Welfare, Springer, vol. 38(1), pages 85-100, January.
    4. Conrado Manuel & Enrique Gonzalez-Aranguena & Rene van den Brink|, 2012. "Players Indifferent to Cooperate and Characterizations of the Shapley Value," Tinbergen Institute Discussion Papers 12-036/1, Tinbergen Institute.
    5. repec:dgr:uvatin:2012105 is not listed on IDEAS
    6. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Axioms of invariance for TU-games," MPRA Paper 41530, University Library of Munich, Germany.
    7. Yan-An Hwang & Yu-Hsien Liao, 2010. "Consistency and dynamic approach of indexes," Social Choice and Welfare, Springer, vol. 34(4), pages 679-694, April.
    8. Genjiu Xu & Ren� van den Brink & Gerard van der Laan & Hao Sun, 2012. "Associated Consistency Characterization of Two Linear Values for TU Games by Matrix Approach," Tinbergen Institute Discussion Papers 12-105/II, Tinbergen Institute.
    9. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.
    10. repec:dgr:uvatin:2012036 is not listed on IDEAS


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