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Linear symmetric rankings for TU-games

Author

Listed:
  • L. Hernández-Lamoneda

    (Centro de Investigación en Matemáticas, A.C.)

  • F. Sánchez-Sánchez

    (Centro de Investigación en Matemáticas, A.C.)

Abstract

We define ranking as an equivalence relation on the set of power indices and study those that have a linear and symmetric representative. Moreover, we classify—or parametrize—those rankings that reward “positive” payoffs for “positive” participation. It is shown that these are in 1-1 correspondence with the points of the standard simplex. Moreover, this correspondence is convex. Finally, we contrast this classification with Saari–Sieberg’s approach via “positive” semi-values.

Suggested Citation

  • L. Hernández-Lamoneda & F. Sánchez-Sánchez, 2017. "Linear symmetric rankings for TU-games," Theory and Decision, Springer, vol. 82(4), pages 461-484, April.
    • Handle: RePEc:kap:theord:v:82:y:2017:i:4:d:10.1007_s11238-016-9576-6
    DOI: 10.1007/s11238-016-9576-6
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    References listed on IDEAS

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    1. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    2. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    3. Josep Freixas, 2010. "On ordinal equivalence of the Shapley and Banzhaf values for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 513-527, October.
    4. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    5. 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.
    6. Ruiz, Luis M & Valenciano, Federico & Zarzuelo, Jose M, 1996. "The Least Square Prenucleolus and the Least Square Nucleolus. Two Values for TU Games Based on the Excess Vector," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 113-134.
    7. Jane Friedman & Lynn Mcgrath & Cameron Parker, 2006. "Achievable Hierarchies In Voting Games," Theory and Decision, Springer, vol. 61(4), pages 305-318, December.
    8. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    9. Saari, Donald G. & Sieberg, Katri K., 2001. "Some Surprising Properties of Power Indices," Games and Economic Behavior, Elsevier, vol. 36(2), pages 241-263, August.
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    Keywords

    Ranking; Linear power index;

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