A concept of an egalitarian solution is developed within the framework of cooperative game theory. The solution is designed to capture the interplay between social values (in this case, egalitarianism) and individual behavior. Both the final outcomes possible coalitional deviations are constrained by these social norms. The authors' main result: despite using a partial order (the Lorenz criterion) to compare allocations, their solution concept yields at most one allocation for each game. The concept is illustrated by a detailed study of convex games, and by a number of examples and applications. Copyright 1989 by The Econometric Society.