Characterizations of the Egalitarian Solution for Convex Games

The egalitarian solution for TU-games as introduced by Dutta and Ray [3] is studied. Two characterizations of the restriction of this solution to the class of convex games are given, using weak variants of the reduced game properties of Hart and Mas-Colell [6] and Davis and Maschler [5]. The other properties are a stability property, inspired by Selten [8], and a property restricting maximum payoffs. Further, a dual egalitarian solution is introduced and it is proved that for a convex game the egalitarian allocation is equal to the dual egalitarian allocation for its dual concave game.