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A monotonic core solution for convex TU games

Author

Listed:
  • J. Arin

    (University of the Basque Country)

  • I. Katsev

    (St Petersburg Institute for Economics and Mathematics)

Abstract

We find that the answer to the open question of whether there is a continuous core solution that satisfies coalitional monotonicity in the class of convex games is yes. We prove that the SD-prenucleolus is a continuous core solution that satisfies coalitional monotonicity for convex games, a class of games widely used to model economic situations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:45:y:2016:i:4:d:10.1007_s00182-015-0500-z
    DOI: 10.1007/s00182-015-0500-z
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    References listed on IDEAS

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    1. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    2. J. Arin & I. Katsev, 2014. "The SD-prenucleolus for TU games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 307-327, December.
    3. J. Arin, 2013. "Monotonic core solutions: beyond Young’s theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 325-337, May.
    4. Katsev, Ilya & Arin Aguirre, Francisco Javier, 2011. "The SD-prenucleolus for TU games," IKERLANAK 2011-56, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    5. Kleppe, J., 2010. "Modelling interactive behaviour, and solution concepts," Other publications TiSEM b9b96884-5761-48f0-9ee4-4, Tilburg University, School of Economics and Management.
    6. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. 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.
    8. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
    9. Arin, Javier & Inarra, Elena, 1998. "A Characterization of the Nucleolus for Convex Games," Games and Economic Behavior, Elsevier, vol. 23(1), pages 12-24, April.
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    Cited by:

    1. Arin Aguirre, Francisco Javier & Katsev, Ilya, 2016. "The SD-prekernel for TU games," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.

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    More about this item

    Keywords

    Convex games; Prenucleolus; Core; Monotonicity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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