Monotonicity and egalitarianism

This paper identifies the maximal domain of transferable utility games on which aggregate monotonicity (no player is worse off when the worth of the grand coalition increases) and egalitarian core selection (no other core allocation can be obtained by a transfer from a richer to a poorer player) are compatible, which turns out to be the class of games where the procedural egalitarian solution selects from the core. On this domain, which includes the class of large core games, these two axioms characterize the solution that assigns the core allocation which lexicographically minimizes the maximal payoffs. This solution even satisfies coalitional monotonicity (no member is worse off when the worth of one coalition increases) and strong egalitarian core selection (no other core allocation can be obtained by transfers from richer to poorer players).