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New characterizations of the Shapley value using weak differential marginalities

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  • Shan, Erfang
  • Cui, Zeguang
  • Yu, Bingxin

Abstract

The principle of differential marginality for cooperative games states that the payoff differential of two players does not change whenever their productivity differential, measured by the differentials of their marginal contributions to coalitions containing neither of them, does not change. The hypothesis of differential marginality is satisfied if and only if the two players are symmetric in the difference of the two games under consideration. In this paper we introduce two weakened variants of differential marginality in which symmetric players in the difference of the two games are replaced by mutually dependent players and necessary players, respectively. By combining these weakened versions of differential marginality with the standard axioms: efficiency and either the null player out property or the disjointly productive players property, we provide two new characterizations of the Shapley value for the setting of variable player sets.

Suggested Citation

  • Shan, Erfang & Cui, Zeguang & Yu, Bingxin, 2024. "New characterizations of the Shapley value using weak differential marginalities," Economics Letters, Elsevier, vol. 238(C).
    • Handle: RePEc:eee:ecolet:v:238:y:2024:i:c:s016517652400168x
    DOI: 10.1016/j.econlet.2024.111685
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    References listed on IDEAS

    as
    1. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
    2. Casajus, André & Yokote, Koji, 2017. "Weak differential marginality and the Shapley value," Journal of Economic Theory, Elsevier, vol. 167(C), pages 274-284.
    3. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    4. Besner, Manfred, 2022. "Disjointly productive players and the Shapley value," Games and Economic Behavior, Elsevier, vol. 133(C), pages 109-114.
    5. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU-game; Shapley value; Differential marginality; Mutually dependent players; Necessary players; Disjointly productive players;
    All these keywords.

    JEL classification:

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

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