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

TL;DR

This paper introduces an extension operator method to convert various cooperative game solutions into efficient ones, unifying egalitarian and proportional sharing principles while preserving their normative properties.

Contribution

It proposes a systematic extension operator approach to restore efficiency in cooperative game solutions, unifying egalitarian and proportional sharing methods.

Findings

Characterizes egalitarian and proportional sharing via a unified framework

Develops an efficient extension operator applicable to various TU game solutions

Demonstrates the method's applicability to network and coalition-structured games

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.