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The balanced contributions property for equal contributors

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  • Yokote, Koji
  • Kongo, Takumi
  • Funaki, Yukihiko

Abstract

We introduce a new axiom, which we term the balanced contributions property for equal contributors. This axiom is defined by restricting the requirement of the balanced contributions property (Myerson, 1980) to two players whose contributions to the grand coalition are the same. We prove that this axiom, together with efficiency and weak covariance, characterizes a new class of solutions, termed the r-egalitarian Shapley values. This class subsumes many variants of the Shapley value, e.g., the egalitarian Shapley values and the discounted Shapley values. Our characterization provides a new axiomatic foundation for analyzing variants of the Shapley value in a unified manner.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:113-124
    DOI: 10.1016/j.geb.2017.08.007
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    Cited by:

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    2. Casajus, André, 2021. "Weakly balanced contributions and the weighted Shapley values," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    3. De, Arijit & Ray, Ankita & Kundu, Tanmoy & Sheu, Jiuh-Biing, 2023. "Is it wise to compete or to collaborate? Remanufacturing business models under collective extended producer responsibility legislation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    4. Guangming Wang & Zeguang Cui & Erfang Shan, 2022. "An Axiomatization of the Value α for Games Restricted by Augmenting Systems," Mathematics, MDPI, vol. 10(15), pages 1-9, August.
    5. Koji Yokote & Takumi Kongo & Yukihiko Funaki, 2021. "Redistribution to the less productive: parallel characterizations of the egalitarian Shapley and consensus values," Theory and Decision, Springer, vol. 91(1), pages 81-98, July.
    6. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
    7. Lina Mallozzi & Juan Vidal-Puga, 2021. "Uncertainty in cooperative interval games: how Hurwicz criterion compatibility leads to egalitarianism," Annals of Operations Research, Springer, vol. 301(1), pages 143-159, June.
    8. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Post-Print hal-03252179, HAL.
    9. Gutiérrez-López, Esther, 2020. "Axiomatic characterizations of the egalitarian solidarity values," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 109-115.
    10. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).
    11. Jun Su & Yuan Liang & Guangmin Wang & Genjiu Xu, 2020. "Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    12. Manuel, C. & Ortega, E. & del Pozo, M., 2020. "Marginality and Myerson values," European Journal of Operational Research, Elsevier, vol. 284(1), pages 301-312.
    13. Koji Yokote & Takumi Kongo & Yukihiko Funaki, 2019. "Relationally equal treatment of equals and affine combinations of values for TU games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 197-212, August.

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    More about this item

    Keywords

    TU games; Balanced contributions property; Shapley value; Axiomatization;
    All these keywords.

    JEL classification:

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

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