Monotonic Solutions to General Cooperative Games
A family of monotonic solutions to general cooperative games (coalitional form games where utility is not assumed to be transferable) is introduced under the name of egalitarian solutions. These solutions generalize the notion that cooperating players within a coalition should have equal compensation for this cooperation where equal compensation is done in interpersonally compared utilities. The egalitarian solutions generalize the weighted Shapley values defined on the subclass of cooperative games with transferable utility and Kalai's proportional solutions defined on the subclass of bargaining games. It is shown that in the presence of other weak axioms the egalitarian solutions are the only monotonic ones. The monotonicity condition is shown to be necessary and sufficient to bring about full cooperation if we assume that the players are individual utility maximizers and can control their levels of cooperation.