The weighted-egalitarian Shapley values

Abstract

We propose a new class of allocation rules for cooperative games with transferable utility (TU-games), weighted-egalitarian Shapley values, where each rule in this class takes into account each player’s contributions and heterogeneity among players to determine each player’s allocation. We provide an axiomatic foundation for the rules with a given weight profile (i.e., exogenous weights) and the class of rules (i.e., endogenous weights). The axiomatization results illustrate the differences among our class of rules, the Shapley value, the egalitarian Shapley values, and the weighted Shapley values.