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Veto players, the kernel of the Shapley value and its characterization

Author

Listed:
  • Sylvain Béal

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Eric Rémila

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this article, we provide a new basis for the kernel of the Shapley value (Shapley, 1953), which is used to construct a new axiom of invariance, and to provide a new axiomatic characterization of the Shapley value. This characterization only invokes marginalistic principles, and does not rely on classical axioms such as symmetry, efficiency or linearity. Moreover, our approach reveals a new instructive role played by veto players.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2014. "Veto players, the kernel of the Shapley value and its characterization," Working Papers hal-01377927, HAL.
    • Handle: RePEc:hal:wpaper:hal-01377927
    Note: View the original document on HAL open archive server: https://hal.science/hal-01377927
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    References listed on IDEAS

    as
    1. Ulrich Faigle & Michel Grabisch, 2014. "Linear Transforms, Values and Least Square Approximation for Cooperation Systems," Documents de travail du Centre d'Economie de la Sorbonne 14010, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    3. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    4. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    5. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    6. Norman L. Kleinberg & Jeffrey H. Weiss, 1985. "Equivalent N -Person Games and the Null Space of the Shapley Value," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 233-243, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Veto players; Addition invariance; Basis; Kernel; Shapley value;
    All these keywords.

    JEL classification:

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

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