Axiomatizations of Dutta-Ray’s Egalitarian Solution on the Domain of Convex Games

We show that on the domain of convex games, Dutta-Ray's egalitarian solution is characterized by core selection, aggregate monotonicity, and bounded richness, a new property requiring that the poorest players cannot be made richer within the core. Replacing "poorest" by "poorer" allows to eliminate aggregate monotonicity. Moreover, strengthening core selection into bilateral consistency a la Davis and Maschler, and Pareto optimality into individual rationality and bilateral consistency a la Hart and Mas-Colell, we obtain alternative and stylized axiomatic approaches.