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Relationally equal treatment of equals and affine combinations of values for TU games

Author

Listed:
  • Koji Yokote

    (Waseda University)

  • Takumi Kongo

    (Fukuoka University)

  • Yukihiko Funaki

    (Waseda University)

Abstract

We axiomatize the set of affine combinations between the Shapley value, the equal surplus division value, and the equal division value in cooperative games with transferable utilities. The set is characterized by efficiency, linearity, the balanced contributions property for equal contributors and outsiders, and the differential null player out property. The balanced contributions property for equal contributors and outsiders requires the balance of contributions between two players who contribute the same amount to the grand coalition and whose singleton coalitions earn the same worth. The differential null player out property requires that an elimination of a null player affects the other players identically. These two relational axioms are obtained by investigating Myerson’s (Int J Game Theory 9:169–182, 1980) balanced contributions property and Derks and Haller’s (Int Game Theory Rev 1:301–314, 1999) null player out property, respectively, from the perspective of a principle of Aristotle’s distributive justice, whereby “equals should be treated equally”.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:53:y:2019:i:2:d:10.1007_s00355-019-01180-y
    DOI: 10.1007/s00355-019-01180-y
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    References listed on IDEAS

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    Cited by:

    1. Casajus, André, 2021. "Weakly balanced contributions and the weighted Shapley values," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    2. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
    3. Takumi Kongo, 2024. "Equal support from others for unproductive players: efficient and linear values that satisfy the equal treatment and weak null player out properties for cooperative games," Annals of Operations Research, Springer, vol. 338(2), pages 973-989, July.
    4. 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.
    5. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).
    6. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.

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    More about this item

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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