We show that on the domain of convex games, Dutta-Ray's egalitarian solution is characterized by core selection, aggregate monotonicity, and bounded richness, a new property requiring that the poorest players cannot be made richer within the core. Replacing "poorest" by "poorer" allows to...

We introduce the constrained egalitarian surplus-sharing rule fCE, which distributes an amount of a divisible resource so that the poorer agents' resulting payoffs become equal but not larger than any remaining agent's status quo payoff. We show that fCE is characterized by Pareto optimality,...

A solution on a set of transferable utility (TU) games satisfies strong aggregate monotonicity (SAM) if every player can improve when the grand coalition becomes richer. It satisfies equal surplus division (ESD) if the solution allows the players to improve equally. We show that the set of...