A Characterization of Maximum Nash Welfare for Indivisible Goods

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 in the simplest setting of two agents.