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Membership separability: A new axiomatization of the Shapley value

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  • de Clippel, Geoffroy

Abstract

The paper shows that Shapley's axiomatic characterization of his value can be strengthened considerably. Indeed, his additivity axiom can be replaced by a simple accounting property whereby a player's payoff is the difference of a reward based on the worth of coalitions to which she belongs, and a tax based on the worth of coalition to which she does not belong, without placing any restriction whatsoever on the functional relationship between the reward or the tax and the worths that determine them.

Suggested Citation

  • de Clippel, Geoffroy, 2018. "Membership separability: A new axiomatization of the Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 125-129.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:125-129
    DOI: 10.1016/j.geb.2017.09.004
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    References listed on IDEAS

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    1. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.
    2. Sylvain Béal & Eric Rémila & Philippe Solal, 2012. "Compensations in the Shapley value and the compensation solutions for graph games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 157-178, February.
    3. Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 279-289.
    4. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    5. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 179-186.
    7. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    8. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2016. "Axiomatic characterizations under players nullification," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 47-57.
    9. Yoshio Kamijo & Takumi Kongo, 2010. "Axiomatization of the Shapley value using the balanced cycle contributions property," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 563-571, October.
    10. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
    11. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
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    Cited by:

    1. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Working Papers 2020-01, CRESE.
    2. Shin Kobayashi, 2021. "A Characterization of the Shapley Value based on “Equal Excess"," Working Papers 2120, Waseda University, Faculty of Political Science and Economics.

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    More about this item

    Keywords

    Cooperative games; Shapley value; Axioms;
    All these keywords.

    JEL classification:

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

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