Approximate maximin shares for groups of agents

Suksompong, Warut

doi:10.1016/j.mathsocsci.2017.09.004

Cited by 52 publications

(32 citation statements)

References 29 publications

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“…Maximin-share has received a lot of attention over the past few years [22,12,1,13,18,11,25,2,6]. The counter-example suggested by Procaccia and Wang [22] refutes the existence of any allocation with the maximin-share guarantee.…”

Section: Related Workmentioning

confidence: 99%

“…They introduce the weighted-maximin-share (WMMS) criterion and propose an allocation algorithm with a 1/2-WMMS guarantee. Suksompong [25] considers the case that the items must be allocated to groups of agents. Gourvès and Monnot [13] extend maximin-share to the case that the goods collectively received by the agents satisfy a matroidal constraint and propose an allocation with a 1/2 maximin-share guarantee.…”

Section: Related Workmentioning

confidence: 99%

“…envy-freeness) in cake-cutting (see among many others, [5,23,24,9,3,4]), moving beyond the metaphor of cake the problem becomes more subtle. For example, when the resource is a set of indivisible goods, a proportional allocation is not guaranteed to exist for all instances 1 For allocation of indivisible goods, Budish [8] introduced a new fairness criterion, namely maximin-share, that attracted a lot of attention in recent years [1,22,18,12,25]. This notion is a relaxation of proportionality for the case of indivisible items.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fair Allocation of Indivisible Goods

Ghodsi

Hajiaghayi

Seddighin

et al. 2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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One of the important yet insufficiently studied subjects in fair allocation is the externality effect among agents. For a resource allocation problem, externalities imply that a bundle allocated to an agent may affect the utilities of other agents.In this paper, we conduct a study of fair allocation of indivisible goods when the externalities are not negligible. We present a simple and natural model, namely network externalities, to capture the externalities. To evaluate fairness in the network externalities model, we generalize the idea behind the notion of maximin-share (MMS) to achieve a new criterion, namely, extendedmaximin-share (EMMS). Next, we consider two problems concerning our model.First, we discuss the computational aspects of finding the value of EMMS for every agent. For this, we introduce a generalized form of partitioning problem that includes many famous partitioning problems such as maximin, minimax, and leximin partitioning problems. We show that a 1/2-approximation algorithm exists for this partitioning problem.Next, we investigate on finding approximately optimal EMMS allocations. That is, allocations that guarantee every agent a utility of at least a fraction of his extended-maximin-share. We show that under a natural assumption that the agents are α-self-reliant, an α/2-EMMS allocation always exists. The combination of this with the former result yields a polynomial-time α/4-EMMS allocation algorithm. 1 arXiv:1805.06191v1 [cs.GT] 16 May 2018 Our Results and TechniquesIn this paper, we take one step toward understanding the impact of externalities in allocation of indivisible items. We start by proposing a general model to capture the externalities in a fair allocation problem under additive assumptions. Although we present some of our results with regard to this general model, the main focus of the paper is on a more restricted model, namely network externalities, where the influences imposed by the agents can be represented by a weighted directed graph. This model is inspired by the well-studied linear-threshold model in the context of network diffusion.We suggest the extended-maximin-share notion (EMMS) to adapt maximin-share to the environment with externalities. Similar to maximin-share, our extension is motivated by the maximin strategy in cut-and-choose games. We discuss two aspects of our notion.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fair Allocation of Indivisible Goods

Ghodsi

Hajiaghayi

Seddighin

et al. 2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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“…Other group fairness notions are based on the idea that the bundle of each group should be perceived as fair by as many agents in the group as possible (e.g. unanimously envyfreeness, h-democratic fairness, majority envy-freeness) [34,39]. The authors suppose that the groups are disjoint and known (e.g.…”

Section: Related Workmentioning

confidence: 99%

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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“…Later on, introduced the notions of EFX and PMMS, and even more recently, proposed to study GMMS allocations. Further variants and generalizations of the criteria we present here have also been considered, see e.g., (Suksompong 2018).…”

Section: Introductionmentioning

confidence: 99%

Multiple Birds with One Stone: Beating 1/2 for EFX and GMMS via Envy Cycle Elimination

Amanatidis

Markakis

Ntokos

2020

AAAI

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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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Approximate maximin shares for groups of agents

Cited by 52 publications

References 29 publications

Fair Allocation of Indivisible Goods

Fair Allocation of Indivisible Goods

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

Multiple Birds with One Stone: Beating 1/2 for EFX and GMMS via Envy Cycle Elimination

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