Article ID: | iaor20001686 |
Country: | Germany |
Volume: | 28 |
Issue: | 2 |
Start Page Number: | 173 |
End Page Number: | 187 |
Publication Date: | Jan 1999 |
Journal: | International Journal of Game Theory |
Authors: | Derks J., Haller H. |
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 multiplicative formula for the weights of the multi-player coalitions and a restrictive condition on the weights of one-player coalitions.