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Weighted nucleoli


  • Hans Haller

    () (Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0316, USA)

  • Jean Derks

    () (Department of Mathematics, Faculty of General Sciences, University of Maastricht, P.O. Box 616, 6200 MD Maastricht, The Netherlands)


Cooperative games in characteristic function form (TU games) are considered. We allow for variable populations or carriers. Weighted nucleoli are defined via weighted excesses for coalitions. A solution satisfies the Null Player Out (NPO) property, if elimination of a null player does not affect the payoffs of the other players. For any single-valued and efficient solution, the NPO property implies the null player property. We show that a weighted nucleolus has the null player property if and only if the weights of multi-player coalitions are weakly decreasing with respect to coalition inclusion. Weighted nucleoli possessing the NPO-property can be characterized by means of a multiplicative formula for the weights of the multi-player coalitions and a restrictive condition on the weights of one-player coalitions.

Suggested Citation

  • Hans Haller & Jean Derks, 1999. "Weighted nucleoli," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 173-187.
  • Handle: RePEc:spr:jogath:v:28:y:1999:i:2:p:173-187
    Note: Received: March 1997/Final version: November 1998

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    Cited by:

    1. Lohmann, E. & Borm, P. & Herings, P.J.J., 2012. "Minimal exact balancedness," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 127-135.
    2. Hokari, Toru, 2005. "Consistency implies equal treatment in TU-games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 63-82, April.
    3. Kleppe, J. & Reijnierse, J.H. & Sudhölter, P., 2013. "Axiomatizations Of Symmetrically Weighted Solutions," Discussion Paper 2013-007, Tilburg University, Center for Economic Research.
    4. Pedro Calleja & Carles Rafels & Stef Tijs, 2012. "Aggregate monotonic stable single-valued solutions for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 899-913, November.
    5. Pedro Calleja & Carles Rafels & Stef Tijs, 2010. "Aggregate monotonic stable single-valued solutions for cooperative games," Working Papers in Economics 237, Universitat de Barcelona. Espai de Recerca en Economia.


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