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arXiv · 2610.29201

Pareto Inefficiency of EFX

Sepideh Mahabadi·Prasanna Ramakrishnan·Jakub Tarnawski
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Abstract

We consider the problem of allocating indivisible goods to agents with additive valuations, under two classic notions of fairness and efficiency: envy-freeness up to any good (EFX) and Pareto optimality. While some of the earliest work on EFX showed that Pareto optimal EFX allocations may not exist if agents can have zero value for some goods, it has remained open whether the same is true when all values are positive. We present a simple instance in which every good has positive value to every agent, but no Pareto optimal EFX allocation exists. We then generalize to a family of instances showing that Pareto optimal $α$-EFX allocations may not exist for any $α> 2/3$.

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Sepideh Mahabadi, Prasanna Ramakrishnan, Jakub Tarnawski. 2026-10-21. Pareto Inefficiency of EFX. https://arxiv.org/abs/2610.29201

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