Weighted Nucleoli

Posted: 6 Aug 1999

See all articles by Jean Derks

Jean Derks

Maastricht University - Department of Mathematics

Hans H. Haller

Virginia Polytechnic Institute & State University - Department of Economics

Abstract

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.

JEL Classification: C71

Suggested Citation

Derks, Jean and Haller, Hans H., Weighted Nucleoli. Available at SSRN: https://ssrn.com/abstract=165450

Jean Derks (Contact Author)

Maastricht University - Department of Mathematics ( email )

Maastricht, 6200 MD
Netherlands
++31 43 38 83502 (Phone)
++31 43 38 84910 (Fax)

Hans H. Haller

Virginia Polytechnic Institute & State University - Department of Economics ( email )

3021 Pamplin Hall
Blacksburg, VA 24061
United States
540-231-7591 (Phone)
540-231-5097 (Fax)

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