The egalitarian solution for convex games : some characterizations

The egalitarian solution for TU-games as introduced by Dutta and Ray [Dutta, B., Ray, D., 1989. A concept of egalitarianism under participation constraints, Econometrica 57, 615–635] is studied. Five characterizations of the restriction of this solution to the class of convex games are given. They all involve a stability property due to the concept of the equal division core from Selten [Selten, R., 1972. Equal share analysis of characteristic function experiments. In: Sauermann, H. (Ed.), Beiträge zur experimentellen Wirtschaftsforschung, Vol. 3, J.C.B. Mohr, Tübingen, pp. 130–165] and all but the third characterization involve a property restricting maximum payoffs. The first two characterizations use in addition efficiency and the reduced game properties of Hart and Mas-Colell [Hart, S., Mas-Colell, A., 1989. Potential, value and consistency. Econometrica 57, 589–614] and Davis and Maschler [Davis, M., Maschler, M., 1965. The kernel of a cooperative game. Naval Research Logistics Quarterly 12, 223–259], respectively. The fourth and fifth characterization only need in addition weak variants of the reduced game properties mentioned above. The third characterization involves besides the stability condition, efficiency and a new consistency property.