Characterizing Maximum Nash Welfare: Envy-Freeness and Proportionality

Karen Frilya Celine, Warut Suksompong and Nicholas Teh

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Abstract: When allocating indivisible goods, the maximum Nash welfare rule is known to be the unique welfarist rule satisfying envy-freeness up to one good. We strengthen this characterization by showing that envy-freeness up to one good can be replaced by substantially weaker fairness requirements: envy-freeness up to $k$ goods or proportionality up to $k$ goods, for any fixed $k$. Our characterization holds even for profiles with identical goods.

Date: 2026-10
New Economics Papers: this item is included in nep-des and nep-mic
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Published in Economics Letters, 269:113310 (2026)

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