The Value of Information Concealment

Fu, Hu; Liaw, Chris; Lu, Pinyan; Tang, Zhihao Gavin

doi:10.1137/1.9781611975031.162

Cited by 11 publications

(7 citation statements)

References 24 publications

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“…Finally, it is worth noting that recent work follows two approaches to derive revenue upper bounds in these works. Some (including this paper) use virtual value theory [CHK07, CHMS10, RTCY12, CMS15, CDW16, CZ17, EFF + 17a, EFF + 17b, LP18,FLLT18]. Others use a more direct probabilitistic approach [HN17, LY13, BILW14, Yao15, RW15, CM16, BGN17, FFR18].…”

Section: Connection To Related Workmentioning

confidence: 99%

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

Beyhaghi

Weinberg

2019

Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

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The Competition Complexity of an auction setting refers to the number of additional bidders necessary in order for the (deterministic, prior-independent, dominant strategy truthful) Vickrey-Clarke-Groves mechanism to achieve greater revenue than the (randomized, priordependent, Bayesian-truthful) optimal mechanism without the additional bidders.We prove that the competition complexity of n bidders with additive valuations over m independent items is at most n(ln(1 + m/n) + 2), and also at most 9 √ nm. When n ≤ m, the first bound is optimal up to constant factors, even when the items are i.i.d. and regular. When n ≥ m, the second bound is optimal for the benchmark introduced in [EFF + 17a] up to constant factors, even when the items are i.i.d. and regular. We further show that, while the Eden et al. benchmark is not necessarily tight in the n ≥ m regime, the competition complexity of n bidders with additive valuations over even 2 i.i.d. regular items is indeed ω(1).Our main technical contribution is a reduction from analyzing the Eden et al. benchmark to proving stochastic dominance of certain random variables.

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Section: Connection To Related Workmentioning

confidence: 99%

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

Beyhaghi

Weinberg

2019

Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

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“…Ronen shows that for any single-item setting, 2RonenRev(D) ≥ DSICRev(D). Fu et al [18] show that RonenRev(D) does not generally guarantee any finite approximation to BICRev(D), but that under some assumptions it attains a 5-approximation. 5 Models.…”

Section: Preliminariesmentioning

confidence: 99%

“…Contrast this with Bayesian truthful, where it is in each buyer's interest to report their true value as long as the other buyers do so as well. Note that we cannot hope to replace DSICRev(D) with BICRev(D) here due to[18] see Section 2 for further discussion.…”

mentioning

confidence: 99%

Smoothed Analysis of Multi-Item Auctions with Correlated Values

Psomas

Schvartzman

Weinberg

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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Consider a seller with m heterogeneous items for sale to a single additive buyer whose values for the items are arbitrarily correlated. It was previously shown that, in such settings, distributions exist for which the seller's optimal revenue is infinite, but the best "simple" mechanism achieves revenue at most one (Briest et al. [5], Hart and Nisan [22]), even when m = 2. This result has long served as a cautionary tale discouraging the study of multi-item auctions without some notion of "independent items".In this work we initiate a smoothed analysis of such multi-item auction settings. We consider a buyer whose item values are drawn from an arbitrarily correlated multi-dimensional distribution then randomly perturbed with magnitude δ under several natural perturbation models. On one hand, we prove that the [5,22] construction is surprisingly robust to certain natural perturbations of this form, and the infinite gap remains.On the other hand, we provide a smoothed model such that the approximation guarantee of simple mechanisms is smoothed-finite. We show that when the perturbation has magnitude δ, pricing only the grand bundle guarantees an O(1/δ)-approximation to the optimal revenue. That is, no matter the (worst-case) initially correlated distribution, these tiny perturbations suffice to bring the gap down from infinite to finite. We further show that the same guarantees hold when n buyers have values drawn from an arbitrarily correlated mn-dimensional distribution (without any dependence on n).Taken together, these analyses further pin down key properties of correlated distributions that result in large gaps between simplicity and optimality.

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“…Of the vast array of works that use the Lagrangian duality framework to achieve an upper bound for approximation [Cai et al, 2016;Brustle, Cai, Wu, and Zhao, 2017;Eden et al, 2017b,a;Fu, Liaw, Lu, and Tang, 2017;Liu and Psomas, 2017], the standard approach used by almost all of them is to select dual variables for the setting at hand that naturally split the upper bound into terms that can be bounded by a few simple mechanisms. Then, the bulk of the work remains in bounding the unique terms with the correct mechanisms.…”

Section: Proof Of the Benchmarkmentioning

confidence: 99%

Simple and Approximately Optimal Pricing for Proportional Complementarities

Cai

Devanur

Goldner

et al. 2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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We study a new model of complementary valuations, which we call "proportional complementarities." In contrast to common models, such as hypergraphic valuations, in our model, we do not assume that the extra value derived from owning a set of items is independent of the buyer's base valuations for the items. Instead, we model the complementarities as proportional to the buyer's base valuations, and these proportionalities are known market parameters.Our goal is to design a simple pricing scheme that, for a single buyer with proportional complementarities, yields approximately optimal revenue. We define a new class of mechanisms where some number of items are given away for free, and the remaining items are sold separately at inflated prices. We find that the better of such a mechanism and selling the grand bundle earns a 12-approximation to the optimal revenue for pairwise proportional complementarities. This confirms the intuition that items should not be sold completely separately in the presence of complementarities. In the more general case, a buyer has a maximum of proportional positive hypergraphic valuations, where a hyperedge in a given hypergraph describes the boost to the buyer's value for item i given by owning any set of items T in addition. The maximum-outdegree of such a hypergraph is d, and k is the positive rank of the hypergraph. For valuations given by these parameters, our simple pricing scheme is an O(min{d, k})-approximation.Cloud Services Example: A cloud service provider offers multiple heterogeneous items that are both substitutes and complements. You can purchase a general purpose virtual machine (VM) or a special purpose VM such as a "data science VM"; these are substitutes. You can also purchase an upgrade such as a fast solid state disk-drive (SSD) which would be complementary to either of those VMs.The goal of this work is to understand how a revenue-maximizing seller should price items such as Microsoft Office products or cloud services when facing a buyer with such complementarities. To this end, we introduce a new model of complementarities, design a pricing scheme for this model, and show worst-case approximation guarantees.In recent years, there has been a surge of research activity on optimal combinatorial pricing. This is the problem of determining and pricing bundles of heterogeneous items in order to maximize revenue from selling to a buyer who has a combinatorial valuation function. The theme of the research has been simple vs. optimal, where simple pricing schemes are shown to approximate the optimal (possibly randomized) pricing scheme to within a universal constant multiplicative factor, independent of the number of items. E.g., for additive valuations, where the buyer's valuation for any set of items is just the sum of her valuations for each individual item, Babaioff, Immorlica, Lucier, and Weinberg [2014] show that the revenue from either selling each item separately (srev), or selling the grand bundle of all the items (brev) is a 6-approximation. Similar results have ...

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The Value of Information Concealment

Cited by 11 publications

References 24 publications

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

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

Smoothed Analysis of Multi-Item Auctions with Correlated Values

Simple and Approximately Optimal Pricing for Proportional Complementarities

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