The joint axiomatization of the prenucleolus and the Dutta-Ray solution for convex games

Most of cooperative TU game solutions are covariant with respect to positive linear transformations of individual utilities. However, this property does not take into account interpersonal comparisons of players' payoffs. The constrained egalitarian solution defined by Dutta and Ray [4] for the class of convex TU games, being not covariant, served as a pretext to studying non-covariant solutions. In the paper a weakening of covariance is given in such a manner that, together with some other properties, it characterizes only two solutions – the prenucleolus and the Dutta–Ray solution – on the class of convex TU games.