In this paper we derive characterizations of egalitarian solutions on two subclasses of the class of balanced games. Firstly we show that the dutta–ray solution is the only solution that satisfies symmetry, independence of irrelevant core allocations, and continuity on the class of convex games. Secondly, together with the other two requirements, a strengthening of continuity to monotonicity in the value of the grand coalition turns out to be sufficient for the characterization of the lexicographically maximal solution on the class of large core games.
Arin, J., Kuipers, J., & Vermeulen, A. J. (2003). Some characterizations of egalitarian solutions on classes of TU-games. Mathematical Social Sciences, 46, 327-345. https://doi.org/10.1016/S0165-4896(03)00051-9