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Sign symmetry vs symmetry: Young’s characterization of the Shapley value revisited

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  • Casajus, André

Abstract

We revisit Young’s (Young, 1985) characterization of the Shapley value by efficiency, symmetry, and marginality/strong monotonicity. In particular, we suggest a relaxation of symmetry called sign symmetry. While symmetry requires equally productive players to obtain the same payoffs, sign symmetry only requires their payoffs to have the same sign. It turns out that sign symmetry can take the place of symmetry in Young’s characterization.

Suggested Citation

  • Casajus, André, 2018. "Sign symmetry vs symmetry: Young’s characterization of the Shapley value revisited," Economics Letters, Elsevier, vol. 169(C), pages 59-62.
    • Handle: RePEc:eee:ecolet:v:169:y:2018:i:c:p:59-62
    DOI: 10.1016/j.econlet.2018.05.017
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    Citations

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    Cited by:

    1. Casajus, André, 2019. "Relaxations of symmetry and the weighted Shapley values," Economics Letters, Elsevier, vol. 176(C), pages 75-78.
    2. Manfred Besner, 2020. "Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 193-212, June.
    3. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Post-Print hal-03252179, HAL.
    4. Besner, Manfred, 2022. "The grand surplus value and repeated cooperative cross-games with coalitional collaboration," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    5. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    6. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2020. "Allocating extra revenues from broadcasting sports leagues," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 65-73.
    7. David Lowing & Kevin Techer, 2021. "Marginalism, Egalitarianism and E ciency in Multi-Choice Games," Working Papers halshs-03334056, HAL.
    8. Li, Wenzhong & Xu, Genjiu & van den Brink, René, 2024. "Sign properties and axiomatizations of the weighted division values," Journal of Mathematical Economics, Elsevier, vol. 112(C).

    More about this item

    Keywords

    TU game; Shapley value; Marginality; Strong monotonicity; Symmetry; Sign symmetry; Weak differential monotonicity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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