Multiple Birds with One Stone: Beating 1/2 for EFX and GMMS via Envy Cycle Elimination
Multiple Birds with One Stone: Beating 1/2 for EFX and GMMS via Envy Cycle Elimination
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一石多鸟：通过 Envy Cycle Elimination 击败 EFX 和 GMMS 的 1/2
DOI：
10.1609/aaai.v34i02.5545
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
E. Markakis
中科院分区：
文献类型：
--
作者：
Georgios Amanatidis;Apostolos Ntokos;E. Markakis
由于大多数这些概念缺乏一般存在的结果，在过去十年中引入了几种嫉妒的味道，在不可分割的商品中量身定制工作，我们提出了一种简单的算法，该算法在某种意义上是普遍公平的，因为它返回具有良好近似值的分配，可保证与四个这样的公平说明尤其是。是黄金比率。 /3-Approximation成对最大份额公平（PMM）。当商品数量不超过代理数量超过两个时就存在。
Several relaxations of envy-freeness, tailored to fair division in settings with indivisible goods, have been introduced within the last decade. Due to the lack of general existence results for most of these concepts, great attention has been paid to establishing approximation guarantees. In this work, we propose a simple algorithm that is universally fair in the sense that it returns allocations that have good approximation guarantees with respect to four such fairness notions at once. In particular, this is the first algorithm achieving a (φ−1)-approximation of envy-freeness up to any good (EFX) and a 2/φ+2 -approximation of groupwise maximin share fairness (GMMS), where φ is the golden ratio. The best known approximation factor, in polynomial time, for either one of these fairness notions prior to this work was 1/2. Moreover, the returned allocation achieves envy-freeness up to one good (EF1) and a 2/3-approximation of pairwise maximin share fairness (PMMS). While EFX is our primary focus, we also exhibit how to fine-tune our algorithm and improve further the guarantees for GMMS or PMMS.Finally, we show that GMMS—and thus PMMS and EFX—allocations always exist when the number of goods does not exceed the number of agents by more than two.
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最大纳什福利和有关 EFX 的其他故事
DOI：
10.24963/ijcai.2020/4
发表时间：
2020
期刊：
--
影响因子：
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作者：
Amanatidis G
通讯作者：
Amanatidis G
DOI：
10.1145/3391403.3399526
发表时间：
2019-02
期刊：
Proceedings of the 21st ACM Conference on Economics and Computation
影响因子：
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作者：
J. Garg;Setareh Taki
通讯作者：
J. Garg;Setareh Taki
改进纳什社会福利近似值
影响因子：
5
作者：
McGlaughlin, Peter;Garg, Jugal
通讯作者：
Garg, Jugal
无偿真实分配机制：特征及其对公平性的影响
DOI：
10.48550/arxiv.1705.10706
发表时间：
2017
期刊：
--
影响因子：
--
作者：
Amanatidis G
通讯作者：
Amanatidis G
EFX 存在三个代理
DOI：
10.1145/3391403.3399511
发表时间：
2020
期刊：
EC '20: Proceedings of the 21st ACM Conference on Economics and Computation
影响因子：
--
作者：
Chaudhury, Bhaskar R.;Garg, Jugal;Mehlhorn, Kurt
通讯作者：
Mehlhorn, Kurt