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Associated consistency and Shapley value


  • 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)


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.

Suggested Citation

  • Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 279-289.
  • Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:279-289

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    Cited by:

    1. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
    2. C. Manuel & E. González-Arangüena & R. Brink, 2013. "Players indifferent to cooperate and characterizations of the Shapley value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 1-14, February.
    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2016. "Characterizations of Three Linear Values for TU Games by Associated Consistency: Simple Proofs Using the Jordan Normal Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-21, March.
    4. repec:spr:compst:v:77:y:2013:i:1:p:1-14 is not listed on IDEAS
    5. repec:spr:joptap:v:173:y:2017:i:1:d:10.1007_s10957-017-1092-5 is not listed on IDEAS
    6. Yan-An Hwang & Yu-Hsien Liao, 2010. "Consistency and dynamic approach of indexes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 679-694, April.
    7. Genjiu Xu & René 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.
    8. Theo Driessen, 2010. "Associated consistency and values for TU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 467-482, July.
    9. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    10. Gérard Hamiache, 2012. "A Matrix Approach to TU Games with Coalition and Communication Structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 85-100, January.
    11. Wenna Wang & Hao Sun & Rene (J.R.) van den Brink & Genjiu Xu, 2018. "The family of ideal values for cooperative games," Tinbergen Institute Discussion Papers 18-002/II, Tinbergen Institute.
    12. Sylvain Béal & MIHAI MANEA & Eric Rémila & Phillippe Solal, 2018. "Games With Identical Shapley Values," Working Papers 2018-03, CRESE.
    13. repec:spr:joptap:v::y::i::d:10.1007_s10957-018-1259-8 is not listed on IDEAS
    14. repec:spr:etbull:v:3:y:2015:i:2:d:10.1007_s40505-014-0054-4 is not listed on IDEAS
    15. repec:eee:apmaco:v:315:y:2017:i:c:p:96-112 is not listed on IDEAS
    16. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.
    17. 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.

    More about this item


    Shapley value · associated game · consistency.;

    JEL classification:

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


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