Weighted nucleoli

J. Derks*, H. Haller

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)173-187
Number of pages15
JournalInternational Journal of Game Theory
Publication statusPublished - 1999

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