Deriving Egalitarian and proportional principles from individual monotonicity

The problem of efficient allocation of the grand coalition worth in transferable-utility games boils down to specifying how the surplus is distributed among individuals, in the situation where the individual share is well-defined. We show that the Individual Monotonicity axiom for Equal Surplus, together with Efficiency and Equal Treatment, implies Egalitarian Surplus Sharing, while the same axiom for Equal Ratio implies Proportional Division. The results thus illustrate the common structure in deriving two principles of surplus distribution, egalitarian and proportional, from the Individual Monotonicity axioms. We further show that relaxation of Equal Treatment leads to Weighted Surplus Sharing and Shifted Proportional Division, highlighting the common structure in which Individual Monotonicity characterizes the allocations that can incorporate social objectives of a redistributive nature.