Finding Fair and Efficient Allocations

Barman, Siddharth; Krishnamurthy, Sanath Kumar; Vaish, Rohit

doi:10.1145/3219166.3219176

Cited by 153 publications

(224 citation statements)

References 28 publications

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“…We prove that x * , the allocation returned by SMatch, is Pareto Optimal (PO). Combined with the statement of Theorem 5.4, and a result of [BKV18] which proves that any allocation that satisfies both EF1 and PO approximates NSW with symmetric, additive valuations within a 1.45 factor, we get the required result. An allocation of items x is called Pareto Optimal when there is no other allocation x ′ where every agent gets at least as much utility as in x, and at least one agent gets higher utility.…”

Section: Symmetric Restricted Additive Nswmentioning

confidence: 67%

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Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings

Garg

Kulkarni

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study the problem of approximating maximum Nash social welfare (NSW) when allocating m indivisible items among n asymmetric agents with submodular valuations. The NSW is a well-established notion of fairness and efficiency, defined as the weighted geometric mean of agents' valuations. For special cases of the problem with symmetric agents and additive(-like) valuation functions, approximation algorithms have been designed using approaches customized for these specific settings, and they fail to extend to more general settings. Hence, no approximation algorithm with factor independent of m is known either for asymmetric agents with additive valuations or for symmetric agents beyond additive(-like) valuations.In this paper, we extend our understanding of the NSW problem to far more general settings. Our main contribution is two approximation algorithms for asymmetric agents with additive and submodular valuations respectively. Both algorithms are simple to understand and involve nontrivial modifications of a greedy repeated matchings approach. Allocations of high valued items are done separately by un-matching certain items and re-matching them, by processes that are different in both algorithms. We show that these approaches achieve approximation factors of O(n) and O(n log n) for additive and submodular case respectively, which is independent of the number of items. For additive valuations, our algorithm outputs an allocation that also achieves the fairness property of envy-free up to one item (EF1).Furthermore, we show that the NSW problem under submodular valuations is strictly harder than all currently known settings with an e e−1 factor of the hardness of approximation, even for constantly many agents. For this case, we provide a different approximation algorithm that achieves a factor of e e−1 , hence resolving it completely.

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Section: Symmetric Restricted Additive Nswmentioning

confidence: 67%

“…Algorithm Hardness Algorithm Restricted Additive 1.069 [GHM19] 1.45 [BKV18] [S] 1.069 [GHM19] O Table 1: Summary of results. Every entry has the best known approximation guarantee for the setting followed by the reference, from this paper or otherwise, that establishes it.…”

Section: Symmetric Agents Asymmetric Agents Hardnessmentioning

confidence: 99%

Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings

Garg

Kulkarni

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…The algorithm can be modified to work with input allocations that have sub-optimal Nash welfare. Combined with a ρ-approximation algorithm for maximizing Nash welfare (such as the algorithms of Cole and Gkatzelis [18] or Barman et al [10]), the modified algorithm runs in polynomial-time and computes an EFX allocation that is 2ρ-approximation to the maximum Nash welfare.…”

Section: Donation Of Itemsmentioning

confidence: 99%

“…The popular website Spliddit [25], available at www.spliddit.org, returns such allocations as part of its "Divide goods" application. Following [15], Barman et al [10] investigate whether EF1 and Pareto-optimal allocations can be computed efficiently and present a pseudo-polynomial-time algorithm.…”

Section: Related Workmentioning

confidence: 99%

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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“…Formally, a mechanism is a β-approximation if the utility of each agent is at least a β fraction of her utility in the Nash bargaining solution. Note that, once the valuations of each agent i are adjusted by subtracting o i , then our objective corresponds to the Nash social welfare (NSW), which has recently received a lot of attention in the fair division literature (e.g., Cole and Gkatzelis, 2018;Garg et al, 2018;Caragiannis et al, 2016;Barman et al, 2018;Brânzei et al, 2017). The NSW maximizing outcome is proportionally fair in that it satisfies a multiplicative version of Pareto efficiency, namely, the utility of an agent cannot be increased by a multiplicative factor without decreasing the product of utilities of other agents by a greater multiplicative factor.…”

Section: Introductionmentioning

confidence: 99%

A Truthful Cardinal Mechanism for One-Sided Matching

Abebe¹,

Cole²,

Gkatzelis³

et al. 2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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We revisit the well-studied problem of designing mechanisms for one-sided matching markets, where a set of n agents needs to be matched to a set of n heterogeneous items. Each agent i has a value vi,j for each item j, and these values are private information that the agents may misreport if doing so leads to a preferred outcome. Ensuring that the agents have no incentive to misreport requires a careful design of the matching mechanism, and mechanisms proposed in the literature mitigate this issue by eliciting only the ordinal preferences of the agents, i.e., their ranking of the items from most to least preferred. However, the efficiency guarantees of these mechanisms are based only on weak measures that are oblivious to the underlying values. In this paper we achieve stronger performance guarantees by introducing a mechanism that truthfully elicits the full cardinal preferences of the agents, i.e., all of the vi,j values. We evaluate the performance of this mechanism using the much more demanding Nash bargaining solution as a benchmark, and we prove that our mechanism significantly outperforms all ordinal mechanisms (even non-truthful ones). To prove our approximation bounds, we also study the population monotonicity of the Nash bargaining solution in the context of matching markets, providing both upper and lower bounds which are of independent interest. * Rediet Abebe was supported in part by a Facebook scholarship.

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Finding Fair and Efficient Allocations

Cited by 153 publications

References 28 publications

Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings

Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings

Envy-Freeness Up to Any Item with High Nash Welfare

A Truthful Cardinal Mechanism for One-Sided Matching

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