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Associated Consistency Characterization of Two Linear Values for TU Games by Matrix Approach

Author

Listed:
  • Genjiu Xu

    () (Northwestern Polytechnical University, Xi'an, P.R. China)

  • René van den Brink

    (VU University Amsterdam)

  • Gerard van der Laan

    (VU University Amsterdam)

  • Hao Sun

    (Northwestern Polytechnical University, Xi'an, P.R. China)

Abstract

This discussion paper resulted in a publication in 'Linear Algebra and its Applications' , 2015, 471, 224-240. Hamiache (2001) assigns to every TU game a so-called associated game and then shows that the Shapley value is characterized as the unique solution for TU games satisfying the inessential game property, continuity and associated consistency. The latter notion means that for every game the Shapley value of the associated game is equal to the Shapley value of the game itself. In this paper we show that also the EANS-value as well as the CIS-value are characterized by these three properties for appropriately modified notions of the associated game. This shows that these three values only differ with respect to the associated game. The characterization is obtained by applying the matrix approach as the pivotal technique for characterizing linear values of TU games in terms of associated consistency.

Suggested Citation

  • 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.
  • Handle: RePEc:tin:wpaper:20120105
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    References listed on IDEAS

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    1. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    2. Yan-An Hwang, 2006. "Associated consistency and equal allocation of nonseparable costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 709-719, August.
    3. L. Hernández-Lamoneda & R. Juárez & F. Sánchez-Sánchez, 2007. "Dissection of solutions in cooperative game theory using representation techniques," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(3), pages 395-426, February.
    4. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    5. Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 279-289.
    6. 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.
    7. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    8. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
    9. 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.
    10. repec:wsi:igtrxx:v:12:y:2010:i:02:n:s0219198910002581 is not listed on IDEAS
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    More about this item

    Keywords

    TU games; Shapley value; EANS-value; CIS-value; associated consistency; matrix approach;

    JEL classification:

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

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