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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.

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

Volume (Year): 28 (1999)
Issue (Month): 2 ()
Pages: 173-187

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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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