A class of balanced games, called exact partition games, is introduced. Within this class, it is shown that the egalitarian solution of Dutta and Ray (1989) behaves as in the class of convex games. Moreover, we provide two axiomatic characterization by means of suitable properties such as consistency, rationality and Lorenz-fairness. As a by-product, alternative characterizations of the egalitarian solution over the class of convex games are obtained.