This article introduces a new axiom of intersecting population monotonicity for TU-games as well as a new model. The axiom, alongside efficiency, characterizes the egalitarian value. The new model addresses situations where a number of roles have to be performed by players. Each player have a specific role and coalitions are feasible only if it contains at most one player for each role. We use the new characterization of the egalitarian value for TU-games to obtain the following result in our class of problem: the egalitarian value is the only sharing rule that ensures that each player of the most productive group is better off joining this most productive group. Thus, we characterize the egalitarian value without fairness requirement and show that, for this new class of problem, egalitarianism can provide incentives towards optimal cooperation.