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On a family of values for TU-games generalizing the Shapley value

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  • Radzik, Tadeusz
  • Driessen, Theo

Abstract

In this paper we study a family of efficient, symmetric and linear values for TU-games, described by some formula generalizing the Shapley value. These values appear to have surprising properties described in terms of the axioms: Fair treatment, monotonicity and two types of acceptability. The results obtained are discussed in the context of the Shapley value, the solidarity value, the least square prenucleolus and the consensus value.

Suggested Citation

  • Radzik, Tadeusz & Driessen, Theo, 2013. "On a family of values for TU-games generalizing the Shapley value," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 105-111.
    • Handle: RePEc:eee:matsoc:v:65:y:2013:i:2:p:105-111
    DOI: 10.1016/j.mathsocsci.2012.10.002
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Emilio Calvo, 2008. "Random marginal and random removal values," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 533-563, December.
    4. 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.
    5. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    7. 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.
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    Cited by:

    1. Casajus, André & Huettner, Frank, 2014. "On a class of solidarity values," European Journal of Operational Research, Elsevier, vol. 236(2), pages 583-591.
    2. Borkotokey, Surajit & Choudhury, Dhrubajit & Kumar, Rajnish & Sarangi, Sudipta, 2020. "Consolidating Marginalism and Egalitarianism: A New Value for Transferable Utility Games," QBS Working Paper Series 2020/12, Queen's University Belfast, Queen's Business School.
    3. Yokote, Koji & Kongo, Takumi & Funaki, Yukihiko, 2018. "The balanced contributions property for equal contributors," Games and Economic Behavior, Elsevier, vol. 108(C), pages 113-124.

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