← 研踪 PaperTrailarXiv:2610.29201 · v2
Pareto Inefficiency of EFX
首次提交 2026-10-21 12:45
版本更新 2026-11-03 06:52
雷达观测 2026-11-04 23:40
摘要
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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v2 · 2026-11-03 06:52 · 最新观测版本
Pareto Inefficiency of EFX
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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