Weighted nucleoli (Q1295838)

The authors consider the concept of weighted nucleolus as a solution concept in a cooperative game. Weighted nucleoli are defined by selecting the unique imputation that lexicographically minimizes the maximal weighted excesses for coalitions which are obtained as coalition specific positive multiples of the ordinary excesses corresponding to an imputation. A solution is said to satisfy the \textit{null player out} property if elimination of a null player does not affect the payoffs of the other players. Weighted nucleoli which have the null player property are characterized. Proofs of many of the results in this paper rely on a condition due to \textit{E. Kohlberg} [SIAM J. Appl. Math. 20, 62-66 (1971; Zbl 0228.90060)].