SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1039-1068, January 2020.
The goal of fair division is to distribute resources among competing players in a “fair" way. Envy-freeness is the most extensively studied fairness notion in fair division. Envy-free allocations do not always exist with indivisible goods, motivating the study of relaxed versions of envy-freeness. We study the envy-freeness up to any good (EFX) property, which states that no player prefers the bundle of another player following the removal of any single good, and prove the first general results about this property. We use the leximin solution to show existence of EFX allocations in several contexts, sometimes in conjunction with Pareto optimality. For two players with valuations obeying a mild assumption, one of these results provides stronger guarantees than the currently deployed algorithm on Spliddit, a popular fair division website. Unfortunately, finding the leximin solution can require exponential time. We show that this is necessary by proving an exponential lower bound on the number of value queries needed to identify an EFX allocation, even for two players with identical valuations. We consider both additive and more general valuations, and our work suggests that there is a rich landscape of problems to explore in the fair division of indivisible goods with different classes of player valuations.

中文翻译：

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具有一般估值的几乎羡慕的自由

SIAM离散数学杂志，第34卷，第2期，第1039-1068页，2020年1月。
不幸的是，找到leximin解决方案可能需要花费指数时间。通过证明确定EFX分配所需的价值查询数量的指数下限，即使对于具有相同估值的两个参与者，我们也证明了这一点。我们同时考虑了加性估值和更一般性的估值，我们的工作表明，在公平划分具有不同参与者估值水平的不可分割商品时，有很多问题需要探讨。