Weighted Constrained Egalitarianism in Tu-Games

The constrained egalitarian solution of Dutta and Ray (1989) for TU-games is extended to asymmetric cases, using the notion of weight systems as in Kalai and Samet (1987, 1988). This weighted constrained egalitarian solution is based on the weighted Lorenz-criterion as an inequality measure. It is shown that in general there is at most one such weighted egalitarian solution for TU-games. Existence is proved for the class of convex games. Furthermore, the core of a positive valued convex game is covered by weighted constrained egalitarian solutions