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note: The nucleolus is not aggregate-monotonic on the domain of convex games

Author

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  • Toru Hokari

    (Department of Economics, University of Rochester, Rochester, NY 14627, USA)

Abstract

We show that the nucleolus is not aggregate-monotonic on the domain of convex games, and that this lack of monotonicity holds even if there are as few as four agents.

Suggested Citation

  • Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 133-137.
    • Handle: RePEc:spr:jogath:v:29:y:2000:i:1:p:133-137
    Note: Received May 1999/Revised version December 1999
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    Citations

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    Cited by:

    1. Yanovskaya, E. & Brânzei, R. & Tijs, S.H., 2008. "Monotonicity Problems of Interval Solutions and the Dutta-Ray Solution for Convex Interval Games," Other publications TiSEM 22884fa9-68cc-4b67-8c27-2, Tilburg University, School of Economics and Management.
    2. J. Arin & I. Katsev, 2016. "A monotonic core solution for convex TU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1013-1029, November.
    3. 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.
    4. Hougaard, Jens Leth & Østerdal, Lars Peter, 2010. "Monotonicity of social welfare optima," Games and Economic Behavior, Elsevier, vol. 70(2), pages 392-402, November.
    5. Dietzenbacher, Bas, 2020. "Monotonicity and Egalitarianism (revision of CentER DP 2019-007)," Discussion Paper 2020-003, Tilburg University, Center for Economic Research.
    6. Josep Maria Izquierdo Aznar & Carlos Rafels Pallarola, 2002. "Coalitionally Monotonic Set-solutions for Cooperative TU Games," Working Papers in Economics 75, Universitat de Barcelona. Espai de Recerca en Economia.
    7. Arin Aguirre, Francisco Javier, 2010. "Monotonic core solutions: Beyond Young's theorem," IKERLANAK 6373, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    8. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2021. "Axiomatizations of Dutta-Ray’s egalitarian solution on the domain of convex games," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    9. Josep Maria Izquierdo Aznar, 2003. "Regular Population Monotonic Allocation Schemes and the Core," Working Papers in Economics 110, Universitat de Barcelona. Espai de Recerca en Economia.
    10. Lars Ehlers & Bettina Klaus, 2004. "Resource-monotonicity for house allocation problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 545-560, August.
    11. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2021. "Considerations on the aggregate monotonicity of the nucleolus and the core-center," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 291-325, April.
    12. Pedro Calleja & Carles Rafels & Stef Tijs, 2006. "The Aggregate-Monotonic Core," Working Papers 280, Barcelona School of Economics.
    13. Yair Tauman & Andriy Zapechelnyuk, 2010. "On (non-) monotonicity of cooperative solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 171-175, March.
    14. J. Arin & V. Feltkamp, 2005. "Monotonicity properties of the nucleolus on the domain of veto balanced games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 331-341, December.
    15. 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.
    16. Josep Maria Izquierdo & Carlos Rafels, 2017. "The incentive core in co-investment problems," UB School of Economics Working Papers 2017/369, University of Barcelona School of Economics.
    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. Hans Keiding, 2011. "Maximizing selections from the core of a cooperative game," Journal of Global Optimization, Springer, vol. 50(1), pages 107-118, May.
    19. Dietzenbacher, Bas, 2021. "Monotonicity and egalitarianism," Games and Economic Behavior, Elsevier, vol. 127(C), pages 194-205.
    20. Pedro Calleja & Carles Rafels & Stef Tijs, 2010. "Aggregate monotonic stable single-valued solutions for cooperative games," Working Papers in Economics 237, Universitat de Barcelona. Espai de Recerca en Economia.
    21. 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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