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The Prenucleolus and the Reduced Game Property: Equal Treatment Replaces Anonymity

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  • Orshan, Gooni

Abstract

In his paper, Sobolev (1975) characterized the prenucleolus as the unique solution concept, defined over the class of cooperative games that satisfies single valuedness, anonymity, covariance under strategic equivalence and reduced game property (consistency). In this paper we show that anonymity can be weakened and replaced by a requirement of equal treatment (symmetry).

Suggested Citation

  • Orshan, Gooni, 1993. "The Prenucleolus and the Reduced Game Property: Equal Treatment Replaces Anonymity," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 241-248.
    • Handle: RePEc:spr:jogath:v:22:y:1993:i:3:p:241-48
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    Citations

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    Cited by:

    1. Guni Orshan & Peter Sudhölter, 2012. "Nonsymmetric variants of the prekernel and the prenucleolus," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 809-828, November.
    2. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2012. "Axiomatic and strategic justifications for the constrained equal benefits rule in the airport problem," Games and Economic Behavior, Elsevier, vol. 75(1), pages 185-197.
    3. Guni Orshan & Peter Sudhölter, 2003. "Reconfirming the Prenucleolus," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 283-293, May.
    4. Katsev, Ilya & Yanovskaya, Elena, 2013. "The prenucleolus for games with restricted cooperation," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 56-65.
    5. John Kleppe & Hans Reijnierse & Peter Sudhölter, 2016. "Axiomatizations of symmetrically weighted solutions," Annals of Operations Research, Springer, vol. 243(1), pages 37-53, August.
    6. Gooni Orshan & Peter Sudholter, 2001. "Reconfirming the Prenucleolus," Discussion Paper Series dp267, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    7. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2018. "Monotonicity and weighted prenucleoli: A characterization without consistency," Discussion Papers on Economics 4/2018, University of Southern Denmark, Department of Economics.
    8. Hokari, Toru, 2005. "Consistency implies equal treatment in TU-games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 63-82, April.
    9. Michel Grabisch & Peter Sudhölter, 2016. "Characterizations of solutions for games with precedence constraints," PSE-Ecole d'économie de Paris (Postprint) hal-01297600, HAL.
    10. Sudholter, Peter, 1998. "Axiomatizations of Game Theoretical Solutions for One-Output Cost Sharing Problems," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 142-171, July.
    11. Michel Grabisch & Peter Sudhölter, 2014. "The positive core for games with precedence constraints," Documents de travail du Centre d'Economie de la Sorbonne 14036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. Álvarez-Mozos, Mikel & Ehlers, Lars, 2024. "Externalities and the (pre)nucleolus in cooperative games," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 10-15.
    13. repec:hal:pseose:hal-01297600 is not listed on IDEAS
    14. Calleja, Pere & Llerena Garrés, Francesc, 2016. "Consistency distinguishes the (weighted) Shapley value, the (weighted) surplus division value and the prenucleolus," Working Papers 2072/266577, Universitat Rovira i Virgili, Department of Economics.
    15. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2017. "Coincidence of the Shapley value with other solutions satisfying covariance," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 1-9.
    16. Chang, Chih & Hu, Cheng-Cheng, 2007. "Reduced game and converse consistency," Games and Economic Behavior, Elsevier, vol. 59(2), pages 260-278, May.
    17. Pedro Calleja & Francesc Llerena & Peter Sudhölter, 2020. "Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1056-1068, August.
    18. Alexander Karpov & Semyon Yurkov, 2012. "Generalized bankruptcy problem," HSE Working papers WP BRP 08/FE/2012, National Research University Higher School of Economics.
    19. Pedro Calleja & Francesc Llerena, 2019. "Path monotonicity, consistency and axiomatizations of some weighted solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 287-310, March.

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