A Characterization of Egalitarian and Proportional Sharing Principles: An Efficient Extension Operator Approach

Abstract

Some well-known solutions for cooperative games with transferable utility (TU-games), such as the Banzhaf value, the Myerson value, and the Aumann-Dreze value, fail to satisfy efficiency. Despite their desirable normative properties, this inefficiency motivates the search for a systematic method to restore efficiency while preserving their underlying normative structure. This paper proposes an efficient extension operator as a general approach to restore efficiency by extending any underlying solution to an efficient one. We consider novel axioms for those operators and characterize the egalitarian surplus sharing method and the proportional sharing method in a unified manner. As applications, we demonstrate the generality of our method by developing an efficient-fair extension of solutions for TU games with communication networks, as well as a variant for TU games with coalition structures.