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Gain–loss and new axiomatizations of the Shapley value

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  • Shan, Erfang
  • Cui, Zeguang
  • Lyu, Wenrong

Abstract

The aim of this paper is to provide new axiomatizations of the Shapley value that generalize previous characterizations. The first characterization employs the gain–loss property, sign differential marginality and the dummy player property. In the second axiomatization, we use the axioms of the gain–loss property, sign symmetry, marginality and the inessential game property. Finally, we introduce the sign marginality property and characterize the Shapley value by combining the property with the other properties.

Suggested Citation

  • Shan, Erfang & Cui, Zeguang & Lyu, Wenrong, 2023. "Gain–loss and new axiomatizations of the Shapley value," Economics Letters, Elsevier, vol. 228(C).
    • Handle: RePEc:eee:ecolet:v:228:y:2023:i:c:s0165176523001933
    DOI: 10.1016/j.econlet.2023.111168
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    References listed on IDEAS

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    1. Einy, Ezra & Haimanko, Ori, 2011. "Characterization of the Shapley–Shubik power index without the efficiency axiom," Games and Economic Behavior, Elsevier, vol. 73(2), pages 615-621.
    2. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
    3. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.
    4. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    5. Casajus, André & Yokote, Koji, 2017. "Weak differential marginality and the Shapley value," Journal of Economic Theory, Elsevier, vol. 167(C), pages 274-284.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU-game; Shapley value; Gain–loss; Sign differential marginality; Sign symmetry;
    All these keywords.

    JEL classification:

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

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