Comparing Approximate Relaxations of Envy-Freeness

Amanatidis, Georgios; Birmpas, Georgios; Markakis, Vangelis

doi:10.24963/ijcai.2018/6

Cited by 54 publications

(102 citation statements)

References 15 publications

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“…We make careful use of the idea of donating items and hit many birds with one stone. We present an algorithm that takes an allocation of maximum Nash welfare as input and, after donating some of the items, outputs an allocation of the remaining ones that is EFX and has a Nash 1 The instance is invariant under a cyclic permutation of agents' names and the respective cyclic permutation of all items except the car.…”

Section: Donation Of Itemsmentioning

confidence: 99%

“…In addition, they present an algorithm for computing an 1/2-EFX allocation, where the value of each agent from her bundle is at least half of what the EFX property requires it to be. Caragiannis et al [15] and Amanatidis et al [1] consider different approximations of EFX (namely, approximations of the strongly related pairwise MMS fairness concept).…”

Section: Related Workmentioning

confidence: 99%

“…To prove the lemma, we use Karamata's inequality for the concave function ϕ(x) = ln(1 + x). Namely, we find a sequence of feasible x i 's such that the ordered sequence b (1)…”

Section: Large Marketsmentioning

confidence: 99%

“…On the other hand, the Nash welfare maximizing allocation from the example above can hardly be considered fair, since Bob gets more value than Alice and Carol put together in our symmetric instance 1 . Consider another allocation, where Alice gets the ring for the value of 9, Bob gets the car for the value of 10, while the painting and the necklace go to Carol with the total value of 15.…”

Section: Introductionmentioning

confidence: 96%

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Envy-Freeness Up to Any Item with High Nash Welfare

Caragiannis

Gravin

Huang

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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Several fairness concepts have been proposed recently in attempts to approximate envy-freeness in settings with indivisible goods. Among them, the concept of envy-freeness up to any item (EFX) is arguably the closest to envy-freeness. Unfortunately, EFX allocations are not known to exist except in a few special cases. We make significant progress in this direction. We show that for every instance with additive valuations, there is an EFX allocation of a subset of items with a Nash welfare that is at least half of the maximum possible Nash welfare for the original set of items. That is, after donating some items to a charity, one can distribute the remaining items in a fair way with high efficiency. This bound is proved to be best possible. Our proof is constructive and highlights the importance of maximum Nash welfare allocation. Starting with such an allocation, our algorithm decides which items to donate and redistributes the initial bundles to the agents, eventually obtaining an allocation with the claimed efficiency guarantee. The application of our algorithm to large markets, where the valuations of an agent for every item is relatively small, yields EFX with almost optimal Nash welfare. To the best of our knowledge, this is the first use of large market assumptions in the fair division literature. We also show that our algorithm can be modified to compute, in polynomial-time, EFX allocations that approximate optimal Nash welfare within a factor of at most 2ρ, using a ρ-approximate allocation on input instead of the maximum Nash welfare one.

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Section: Donation Of Itemsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…To prove the lemma, we use Karamata's inequality for the concave function ϕ(x) = ln(1 + x). Namely, we find a sequence of feasible x i 's such that the ordered sequence b (1)…”

Section: Large Marketsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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Envy-Freeness Up to Any Item with High Nash Welfare

Caragiannis

Gravin

Huang

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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“…Note that every additive valuation is responsive. Additive valuations are often assumed in recent fair division literature [Caragiannis et al, 2016;Amanatidis et al, 2018;Biswas and Barman, 2018;Conitzer et al, 2019]. An instance consists of agents, goods, and utility functions (and in the model of Sections 3 and 4, the partition of agents into groups).…”

Section: Preliminariesmentioning

confidence: 99%

Almost Envy-Freeness in Group Resource Allocation

Kyropoulou

Suksompong

Voudouris

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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We study the problem of fairly allocating indivisible goods between groups of agents using the recently introduced relaxations of envy-freeness. We consider the existence of fair allocations under different assumptions on the valuations of the agents. In particular, our results cover cases of arbitrary monotonic, responsive, and additive valuations, while for the case of binary valuations we fully characterize the cardinalities of two groups of agents for which a fair allocation can be guaranteed with respect to both envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX). Moreover, we introduce a new model where the agents are not partitioned into groups in advance, but instead the partition can be chosen in conjunction with the allocation of the goods. In this model, we show that for agents with arbitrary monotonic valuations, there is always a partition of the agents into two groups of any given sizes along with an EF1 allocation of the goods. We also provide an extension of this result to any number of groups.

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Group Envy Freeness and Group Pareto Efficiency in Fair Division with Indivisible Items

Aleksandrov

Walsh

2018

Lecture Notes in Computer Science

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We consider two models of fair division with indivisible items: one for goods and one for bads. For goods, we study two generalized envy freeness proxies (EF1 and EFX for goods) and three common welfare (utilitarian, egalitarian and Nash) efficiency notions. For bads, we study two generalized envy freeness proxies (1EF and XEF for goods) and two less common diswelfare (egalitarian and Nash) efficiency notions. Some existing algorithms for goods do not work for bads. We thus propose several new algorithms for the model with bads. Our new algorithms exhibit many nice properties. For example, with additive identical valuations, an allocation that maximizes the egalitarian diswelfare or Nash diswelfare is XEF and PE. Finally, we also give simple and tractable cases when these envy freeness proxies and welfare efficiency are attainable in combination (e.g. 0/1 valuations, 0/ − 1 valuations, house allocations).

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Comparing Approximate Relaxations of Envy-Freeness

Cited by 54 publications

References 15 publications

Envy-Freeness Up to Any Item with High Nash Welfare

Envy-Freeness Up to Any Item with High Nash Welfare

Almost Envy-Freeness in Group Resource Allocation

Group Envy Freeness and Group Pareto Efficiency in Fair Division with Indivisible Items

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