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The prenucleolus for games with communication structures

Author

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  • Khmelnitskaya, Anna B.

    () (Faculty of Applied Mathematics)

  • Sudhölter, Peter

    () (Department of Business and Economics)

Abstract

t is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented.

Suggested Citation

  • Khmelnitskaya, Anna B. & Sudhölter, Peter, 2011. "The prenucleolus for games with communication structures," Discussion Papers of Business and Economics 10/2011, University of Southern Denmark, Department of Business and Economics.
  • Handle: RePEc:hhs:sdueko:2011_010
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    File URL: https://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2011/dpbe10_2011.pdf
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    References listed on IDEAS

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    1. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z., 2010. "The average tree solution for cooperative games with communication structure," Games and Economic Behavior, Elsevier, vol. 68(2), pages 626-633, March.
    2. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    3. Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 113-136, March.
    4. Bezalel Peleg & Peter Sudholter, 2004. "Bargaining Sets of Voting Games," Discussion Paper Series dp376, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Katsev, Ilya & Yanovskaya, Elena, 2013. "The prenucleolus for games with restricted cooperation," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 56-65.
    6. 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, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU game; solution concept; communication and conference structure; nucleolus;

    JEL classification:

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

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