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Aggregate monotonic stable single-valued solutions for cooperative games

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  • Pedro Calleja

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  • Carles Rafels
  • Stef Tijs
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    Abstract

    This article considers single-valued solutions of transferable utility cooperative games that satisfy core selection and aggregate monotonicity, defined either on the set of all games, G N , or on the set of essential games, E N (those with a non-empty imputation set). The main result is that for an arbitrary set of players, core selection and aggregate monotonicity are compatible with individual rationality, the dummy player property and symmetry for single-valued solutions defined on both G N and E N . This result solves an open question in the literature (see for example Young et al. Water Resour Res 18:463–475, 1982 ). Copyright Springer-Verlag Berlin Heidelberg 2012

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    File URL: http://hdl.handle.net/10.1007/s00182-012-0355-5
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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 41 (2012)
    Issue (Month): 4 (November)
    Pages: 899-913

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    Handle: RePEc:spr:jogath:v:41:y:2012:i:4:p:899-913

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    Related research

    Keywords: Cooperative games; Core; Aggregate monotonicity; Individual rationality; Dummy player property; Symmetry; C71;

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    1. Jens Leth Hougaard & Bezalel Peleg & Lars Peter Østerdal, 2005. "The Dutta-Ray Solution On The Class Of Convex Games: A Generalization And Monotonicity Properties," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 431-442.
    2. Calleja, Pedro & Rafels, Carles & Tijs, Stef, 2009. "The aggregate-monotonic core," Games and Economic Behavior, Elsevier, vol. 66(2), pages 742-748, July.
    3. David Housman & (*), Lori Clark, 1998. "Note Core and monotonic allocation methods," International Journal of Game Theory, Springer, vol. 27(4), pages 611-616.
    4. Kleppe, J., 2010. "Modelling interactive behaviour, and solution concepts," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3763576, Tilburg University.
    5. Hans Haller & Jean Derks, 1999. "Weighted nucleoli," International Journal of Game Theory, Springer, vol. 28(2), pages 173-187.
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