The prenucleolus and the reduced game property: Equal treatment replaces anonymity

In his paper, Sobolev [1975] characterized the prenucleolus as the unique solution concept, defined over the class of cooperative games that satisfies single valuedness, anonymity, covariance under strategic equivalence and reduced game property (consistency). In this paper we show that anonymity can be weakened and replaced by a requirement of equal treatment (symmetry).