NUCLEOLI AS MAXIMIZERS OF COLLECTIVE SATISFACTION FUNCTIONS

Two preimputations of a given TU game can be compared via the Lorenz o rder applied to the vectors of satisfactions. One preimputation is 'so cially more desirable' than the other, if its corresponding vector of satisfactions Lorenz dominates the satisfaction vector with respect to the second preimputation. It is shown that the prenucleolus, the anti -prenucleolus, and the modified nucleolus are maximal in this Lorenz o rder. Here the modified nucleolus is the unique preimputation which le xicographically minimizes the envies between the coalitions, i.e. the differences of excesses. Recently Sudholter developed this solution co ncept. Properties of the set of all undominated preimputations, the ma ximal satisfaction solution, are discussed. A function on the set of p reimputations is called collective satisfaction function if it respect s the Lorenz order. We prove that both classical nucleoli are unique m inimizers of certain 'weighted Gini inequality indices', which are der ived from some collective satisfaction functions. For the (pre)nucleol us the function proposed by Kohlberg, who characterized the nucleolus as a solution of a single minimization problem, can be chosen. Finally , a collective satisfaction function is defined such that the modified nucleolus is its unique maximizer.