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Axiomatic characterizations under players nullification

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])

  • Sylvain Ferrières

    (Leipzig Graduate School of Management)

  • Eric Rémila

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

Abstract

Many axiomatic characterizations of values for cooperative games invoke axioms which evaluate the consequences of removing an arbitrary player. Balanced contributions (Myerson, 1980) and balanced cycle contributions (Kamijo and Kongo, 2010) are two well-known examples of such axioms. We revisit these characterizations by nullifying a player instead of deleting her/him from a game. The nullification (Beal et al., 2014a) of a player is obtained by transforming a game into a new one in which this player is a null player, i.e. the worth of the coalitions containing this player is now identical to that of the same coalition without this player. The degree with which our results are close to the original results in the literature is connected to the fact that the targeted value satisfies the null player out axiom (Derks and Haller, 1999). We also revisit the potential approach (Hart and Mas-Colell, 1989) similarly.

Suggested Citation

  • Sylvain Béal & Sylvain Ferrières & Eric Rémila & Philippe Solal, 2016. "Axiomatic characterizations under players nullification," Post-Print halshs-01293700, HAL.
    • Handle: RePEc:hal:journl:halshs-01293700
    DOI: 10.1016/j.mathsocsci.2016.01.002
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    Citations

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    Cited by:

    1. Kongo, Takumi, 2018. "Balanced contributions based on indirect claims and the Shapley value," Economics Letters, Elsevier, vol. 167(C), pages 48-50.
    2. de Clippel, Geoffroy, 2018. "Membership separability: A new axiomatization of the Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 125-129.
    3. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    4. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    5. Takaaki Abe & Satoshi Nakada, 2023. "Potentials and solutions of cooperative games with a fixed player set," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 757-774, September.
    6. Zou, Zhengxing & van den Brink, René, 2020. "Equal loss under separatorization and egalitarian values," Economics Letters, Elsevier, vol. 194(C).
    7. Yokote, Koji & Kongo, Takumi & Funaki, Yukihiko, 2018. "The balanced contributions property for equal contributors," Games and Economic Behavior, Elsevier, vol. 108(C), pages 113-124.
    8. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).
    9. Sylvain Ferrières, 2016. "Nullified equal loss property and equal division values," Working Papers 2016-06, CRESE.
    10. Zhengxing Zou & René Brink & Yukihiko Funaki, 2022. "Sharing the surplus and proportional values," Theory and Decision, Springer, vol. 93(1), pages 185-217, July.
    11. Ori Haimanko, 2025. "On subgame consistency of the Shapley-Shubik power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(2), pages 1-20, December.
    12. Shan, Erfang & Kang, Liying & Shi, Jilei, 2025. "Modifications of several axiomatizations of the Shapley value by weakening the efficiency axiom," Economics Letters, Elsevier, vol. 256(C).
    13. Ricardo Martínez & Joaquín Sánchez-Soriano, 2026. "Order preservation with dummies in the museum pass problem," Annals of Operations Research, Springer, vol. 356(1), pages 11-29, January.
    14. Ricardo Mart'inez & Joaqu'in S'anchez-Soriano, 2023. "Order preservation with dummies in the musseum pass problem," Papers 2307.00622, arXiv.org.
    15. Zhang, Li & Xu, Genjiu & Sun, Hao & Li, Wenzhong, 2023. "Players’ dummification and the dummified egalitarian non-separable contribution value," Economics Letters, Elsevier, vol. 226(C).
    16. C. Manuel & E. Ortega & M. del Pozo, 2023. "Marginality and the position value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 459-474, July.
    17. Kaneko, Takuto & Nakada, Satoshi, 2025. "Nullified-game consistency and axiomatizations of the Core of TU-games with a fixed player set," Economics Letters, Elsevier, vol. 250(C).
    18. Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "Social solidarity with dummies in the museum pass problem," ThE Papers 21/11, Department of Economic Theory and Economic History of the University of Granada..
    19. Sylvain Ferrières, 2017. "Nullified equal loss property and equal division values," Theory and Decision, Springer, vol. 83(3), pages 385-406, October.
    20. Sylvain Ferrières, 2016. "Smoothness, nullified equal loss property and equal division values," Working Papers 2016-01, CRESE.

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    JEL classification:

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

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