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The prenucleolus for games with communication structures

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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.

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Bibliographic Info

Paper provided by Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 10/2011.

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Length: 15 pages
Date of creation: 10 Dec 2011
Date of revision:
Handle: RePEc:hhs:sdueko:2011_010

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Postal: Department of Business and Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Phone: 65 50 32 33
Fax: 65 50 32 37
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Web page: http://www.sdu.dk/ivoe
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Related research

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

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  1. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2010. "The average tree solution for cooperative games with communication structure," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3736837, Tilburg University.
  2. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  3. Orshan,G. & Sudhoelter,P., 2001. "The positive core of a cooperative game," Working Papers 326, Bielefeld University, Center for Mathematical Economics.
  4. Katsev, Ilya & Yanovskaya, Elena, 2013. "The prenucleolus for games with restricted cooperation," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 56-65.
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