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A note on NTU convexity

Author

Listed:
  • Ruud Hendrickx

    (CentER and Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • Judith Timmer

    (Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands This author acknowledges financial support from the Netherlands Organisation for Scientific Research through project 613-304-059)

  • Peter Borm

    (CentER and Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)

Abstract

For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept. Convexity can be defined in a number of ways, each having its own specific attractions. Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation. For games with nontransferable utility, however, the literature mainly focuses on two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation. In this paper, we analyse three types of convexity for NTU games that generalise the marginalistic interpretation of convexity.

Suggested Citation

  • Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    • Handle: RePEc:spr:jogath:v:31:y:2002:i:1:p:29-37
    Note: Received: December 2000
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    Cited by:

    1. Dietzenbacher, Bas & Yanovskaya, Elena, 2023. "The equal split-off set for NTU-games," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 61-67.
    2. Takuya Masuzawa, 2012. "Strong convexity of NTU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 699-705, August.
    3. Arantza Estévez-Fernández & Peter Borm & M. Gloria Fiestras-Janeiro, 2020. "Nontransferable utility bankruptcy games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 154-177, April.
    4. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    5. Judith Timmer & Peter Borm & Stef Tijs, 2005. "Convexity In Stochastic Cooperative Situations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 25-42.
    6. Koshevoy, G.A. & Suzuki, T. & Talman, A.J.J., 2014. "Supermodular NTU-games," Other publications TiSEM 23321d39-5b97-4a09-b120-6, Tilburg University, School of Economics and Management.
    7. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "Egalitarianism in Nontransferable Utility Games," Discussion Paper 2017-023, Tilburg University, Center for Economic Research.
    8. Takuya Masuzawa, 2008. "Computing the cores of strategic games with punishment–dominance relations," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 185-201, June.
    9. Jesús Getán & Jesús Montes & Carles Rafels, 2014. "A note: characterizations of convex games by means of population monotonic allocation schemes," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 871-879, November.
    10. Pintér, Miklós, 2016. "A cardinal convex game with empty core," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 9-10.
    11. Takuya Masuzawa, 2012. "Punishment-Dominance Condition on Stable Two-Sided Matching Algorithms," Keio/Kyoto Joint Global COE Discussion Paper Series 2012-018, Keio/Kyoto Joint Global COE Program.
    12. Csóka, Péter & Jean-Jacques Herings, P. & Kóczy, László Á. & Pintér, Miklós, 2011. "Convex and exact games with non-transferable utility," European Journal of Operational Research, Elsevier, vol. 209(1), pages 57-62, February.
    13. Luisa Carpente & Balbina Casas-Méndez & Javier Gozálvez & Natividad Llorca & Manuel Pulido & Joaquín Sánchez-Soriano, 2013. "How to divide a cake when people have different metabolism?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(3), pages 361-371, December.

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