Yukihiko Funaki (Waseda university) – Axiomatizations of the egalitarian surplus sharing, the proportional division and the extensions

The problem of efficient allocation of the grand coalition worth in a transferable-utility game 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 the Efficiency and Equal Treatment axioms, 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 Individual Monotonicity axioms. We further show that relaxing the Equal Treatment axiom leads to Weighted Surplus Sharing and Shifted Proportional Division, which are obtained as a result of redistribution of the Equal Surplus and the Equal Ratio, respectively, highlighting once again the central role played by the Individual Monotonicity axioms in characterizing these allocations.