Optimal (and benchmark-optimal) competition complexity for additive buyers over independent items

Beyhaghi, Hedyeh; Weinberg, S. Matthew

doi:10.1145/3313276.3316405

Cited by 13 publications

(11 citation statements)

References 26 publications

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“…The work by Eden et al [2017] found the first such result that beats the optimal revenue for the additive setting, while Feldman et al [2018] improve the bounds on the number of added buyers drastically, but they only recover a (1 − ε)-fraction of the optimal revenue. Very recent work of Beyhaghi and Weinberg [2018] match these bounds in the small market regime and drastically improve the bounds of Eden et al [2017] in the large market regime, even though the [Beyhaghi and Weinberg, 2018] results are for precise coverage of the optimal revenue. While all the above papers presents BK-style results for revenue maximization in one-sided markets, our work presents BK-style results for welfare (and gains from trade) in two-sided markets, which to the best of our knowledge was not suggested or studied in any prior paper.…”

Section: Additional Related Worksupporting

confidence: 54%

Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

Babaioff¹,

Goldner²,

Gonczarowski³

2020

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

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We consider the problem of welfare (and gains-from-trade) maximization in two-sided markets using simple mechanisms that are prior-independent. The seminal impossibility result of Myerson and Satterthwaite [1983] shows that even for bilateral trade, there is no feasible (individually rational, truthful, and budget balanced) mechanism that has welfare as high as the optimal-yet-infeasible VCG mechanism, which attains maximal welfare but runs a deficit. On the other hand, the optimal feasible mechanism needs to be carefully tailored to the Bayesian prior, and even worse, it is known to be extremely complex, eluding a precise description.In this paper we present Bulow-Klemperer-style results to circumvent these hurdles in doubleauction market settings. We suggest using the Buyer Trade Reduction (BTR) mechanism, a variant of McAfee's mechanism, which is feasible and simple (in particular, it is deterministic, truthful, prior-independent, and anonymous). First, in the setting in which the values of the buyers and of the sellers are sampled independently and identically from the same distribution, we show that for any such market of any size, BTR with one additional buyer whose value is sampled from the same distribution has expected welfare at least as high as the optimal-yetinfeasible VCG mechanism in the original market.We then move to a more general setting in which the values of the buyers are sampled from one distribution, and those of the sellers from another, focusing on the case where the buyers' distribution first-order stochastically dominates the sellers' distribution. We present both upper bounds and lower bounds on the number of buyers that, when added, guarantees that BTR in the augmented market have welfare at least as high as the optimal in the original market. Our lower bounds extend to a large class of mechanisms, and all of our positive and negative results extend to adding sellers instead of buyers. In addition, we present positive results about the usefulness of pricing at a sample for welfare maximization (and more precisely, for gains-fromtrade approximation) in two-sided markets under the above two settings, which to the best of our knowledge are the first sampling results in this context. * Microsoft Research 9 Moreover, the result fails even for some pair of regular distributions, a condition that is used in the proof of the BK result.10 In the absence of any prior, it is natural to treat all agents the same, and thus anonymity is a natural assumption, and one may even claim that it is in a sense a prerequisite for simplicity.

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Section: Additional Related Worksupporting

confidence: 54%

Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

Babaioff¹,

Goldner²,

Gonczarowski³

2020

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

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“…In other words, these settings are competitive enough for enhanced competition to not yield great gains in the revenue. Thus, the interesting range of parameters is 1 < n ≪ m. See [BW19] for a related result.…”

Section: Our Resultsmentioning

confidence: 91%

“…One key difference between the current work and the foregoing works is that all of them focus on upper bounding the optimal revenue with n bidders by the revenue of an auction that sells the items separately with n ′ bidders, while we also consider VCG auctions with an entry fee. It is known that when restricting attention to auctions that sell the items separately, one cannot get a bound better than n ′ = n • Ω(log m n ) [FFR18,BW19]. Thus, these works cannot hope to get n ′ = O(n) like we do.…”

Section: Related Workmentioning

confidence: 88%

“…Among the first such works were those of [RTCY20] and [EFF + 17a] which show the bounds n ′ = m and n ′ = O(n + m) for unit-demand and additive bidders respectively. These works were followed by [FFR18] and [BW19] which improve these bounds to n ′ = n • O(log m n ) for additive bidders. We remark that [FFR18] focuses on getting a (1 − ǫ)-fraction of the optimal revenue with n bidders while all the other works outperform the optimal revenue with n bidders.…”

Section: Related Workmentioning

confidence: 99%

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99% Revenue with Constant Enhanced Competition

Cai

Saxena

2021

Preprint

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The enhanced competition paradigm is an attempt at bridging the gap between simple and optimal auctions. In this line of work, given an auction setting with m items and n bidders, the goal is to find the smallest n ′ ≥ n such that selling the items to n ′ bidders through a simple auction generates (almost) the same revenue as the optimal auction.Recently, Feldman, Friedler, and Rubinstein [EC, 2018] showed that an arbitrarily large constant fraction of the optimal revenue from selling m items to a single bidder can be obtained via simple auctions with a constant number of bidders. However, their techniques break down even for two bidders, and can only show a bound of n ′ = n • O(log m n ). Our main result is that n ′ = O(n) bidders suffice for all values of m and n. That is, we show that, for all m and n, an arbitrarily large constant fraction of the optimal revenue from selling m items to n bidders can be obtained via simple auctions with O(n) bidders. Moreover, when the items are regular, we can achieve the same result through auctions that are prior-independent, i.e., they do not depend on the distribution from which the bidders' valuations are sampled.

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“…Each bidder i is has value v ij for item j, and values the set S of items at j∈S v ij . Such valuations are called additive, and are perhaps the most well-studied valuations in multi-item auction design Nisan, 2012, 2013;Li and Yao, 2013;Babaioff et al, 2014;Daskalakis et al, 2014;Hart and Reny, 2015;Cai et al, 2016;Daskalakis et al, 2017b;Beyhaghi and Weinberg, 2019).…”

Section: Auction Design and Symmetriesmentioning

confidence: 99%

A Permutation-Equivariant Neural Network Architecture For Auction Design

Rahme¹,

Jelassi²,

Bruna³

et al. 2020

Preprint

Self Cite

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Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. Theoretical approaches to the problem have hit some limits in the past decades and analytical solutions are known for only a few simple settings. Computational approaches to the problem through the use of LPs have their own set of limitations. Building on the success of deep learning, a new approach was recently proposed by Dütting et al. (2017) in which the auction is modeled by a feed-forward neural network and the design problem is framed as a learning problem. The neural architectures used in that work are general purpose and do not take advantage of any of the symmetries the problem could present, such as permutation equivariance. In this work, we consider auction design problems that have permutation-equivariant symmetry and construct a neural architecture that is capable of perfectly recovering the permutationequivariant optimal mechanism, which we show is not possible with the previous architecture. We demonstrate that permutation-equivariant architectures are not only capable of recovering previous results, they also have better generalization properties.

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Optimal (and benchmark-optimal) competition complexity for additive buyers over independent items

Cited by 13 publications

References 26 publications

Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

99% Revenue with Constant Enhanced Competition

A Permutation-Equivariant Neural Network Architecture For Auction Design

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