A Characterization of Maximum Nash Welfare for Indivisible Goods

TL;DR

This paper characterizes the maximum Nash welfare rule as the unique additive welfarist rule satisfying envy-freeness up to one good, even with only two agents, advancing understanding of fair division of indivisible goods.

Contribution

It provides a unique characterization of MNW as the only additive welfarist rule meeting envy-freeness up to one good in simple two-agent settings.

Findings

MNW is uniquely characterized among additive welfarist rules.

MNW satisfies envy-freeness up to one good.

Characterization holds even with only two agents.

Abstract

In the allocation of indivisible goods, the maximum Nash welfare (MNW) rule, which chooses an allocation maximizing the product of the agents' utilities, has received substantial attention for its fairness. We characterize MNW as the only additive welfarist rule that satisfies envy-freeness up to one good. Our characterization holds even in the simplest setting of two agents.