Supply-limiting mechanisms

Roughgarden, Tim; Talgam-Cohen, Inbal; Yan, Qiqi

doi:10.1145/2229012.2229077

Cited by 42 publications

(32 citation statements)

References 26 publications

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“…For example, previous work has demonstrated that auctions with reasonably good approximation factors are possible with minimal dependence on the valuation distributions (e.g. [9,26,2]) or even, when there is no bidder with a unique valuation distribution, with no dependence on the valuation distributions [17,18,36]. Another interpretation of some previous results, such as [11,9], is the existence of constant-factor approximate auctions that derive no benefit from bidder competition.…”

Section: Our Resultsmentioning

confidence: 90%

The sample complexity of revenue maximization

Cole

Roughgarden

2014

Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing

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In the design and analysis of revenue-maximizing auctions, auction performance is typically measured with respect to a prior distribution over inputs. The most obvious source for such a distribution is past data. The goal of this paper is to understand how much data is necessary and sufficient to guarantee near-optimal expected revenue.Our basic model is a single-item auction in which bidders' valuations are drawn independently from unknown and nonidentical distributions. The seller is given m samples from each of these distributions "for free" and chooses an auction to run on a fresh sample. How large does m need to be, as a function of the number k of bidders and > 0, so that a (1 − )-approximation of the optimal revenue is achievable?We prove that, under standard tail conditions on the underlying distributions, m = poly(k, 1 ) samples are necessary and sufficient. Our lower bound stands in contrast to many recent results on simple and prior-independent auctions and fundamentally involves the interplay between bidder competition, non-identical distributions, and a very close (but still constant) approximation of the optimal revenue. It effectively shows that the only way to achieve a sufficiently good constant approximation of the optimal revenue is through a detailed understanding of bidders' valuation distributions. Our upper bound is constructive and applies in particular to a variant of the empirical Myerson auction, the natural auction that runs the revenue-maximizing auction with respect to the empirical distributions of the samples. To capture how our sample complexity upper bound depends on the set of allowable distributions, we introduce α-strongly regular distributions, which interpolate between the well-studied classes of regular (α = 0) and MHR (α = 1) distributions. We give evidence that this definition is of independent interest.

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Section: Our Resultsmentioning

confidence: 90%

The sample complexity of revenue maximization

Cole

Roughgarden

2014

Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing

Self Cite

188

270

View full text Add to dashboard Cite

show abstract

“…However, it is easy to see there are instances in which the revenue in every competitive equilibrium is 0 (even for unit-demand valuations). A natural approach to revenue extraction is limiting the supply, which has the effect of increasing competition among the consumers [Roughgarden et al, 2012]. However, recall we are dealing with markets that are unstable unless they clear; bundling should thus be done carefully to ensure market clearance.…”

Section: Revenue Maximizationmentioning

confidence: 99%

Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

Dobzinski

Feldman

Talgam-Cohen

et al. 2015

Web and Internet Economics

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We study equilibria of markets with m heterogeneous indivisible goods and n consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes. Given the widespread use of bundling in real-life markets, we study its role as a stabilizing and coordinating device by considering the notion of competitive bundling equilibrium: a competitive equilibrium over the market induced by partitioning the goods for sale into fixed bundles. Compared to other equilibrium concepts involving bundles, this notion has the advantage of simulatneous succinctness (O(m) prices) and market clearance.Our first set of results concern welfare guarantees. We show that in markets where consumers care only about the number of goods they receive (known as multi-unit or homogeneous markets), even in the presence of complementarities, there always exists a competitive bundling equilibrium that guarantees a logarithmic fraction of the optimal welfare, and this guarantee is tight. We also establish non-trivial welfare guarantees for general markets, two-consumer markets, and markets where the consumer valuations are additive up to a fixed budget (budget-additive).Our second set of results concern revenue guarantees. Motivated by the fact that the revenue extracted in a standard competitive equilibrium may be zero (even with simple unit-demand consumers), we show that for natural subclasses of gross substitutes valuations, there always exists a competitive bundling equilibrium that extracts a logarithmic fraction of the optimal welfare, and this guarantee is tight. The notion of competitive bundling equilibrium can thus be useful even in markets which possess a standard competitive equilibrium.

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“…Recently, several prior-independent auctions were studied [e.g. 8,19,10]. These auctions greatly reduce the amount or precision of the knowledge needed by the auctioneer on the prior distribution, while guaranteeing nearly optimal performance against the fully knowledgeable optimal auction.…”

Section: Introductionmentioning

confidence: 99%

Optimal auctions for correlated buyers with sampling

Haghpanah

Hartline

et al. 2014

Proceedings of the Fifteenth ACM Conference on Economics and Computation

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Crémer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer has only incomplete knowledge of the distribution, represented by a finite family of candidate distributions, and has sample access to the real distribution. We show that the naive approach which uses samples to distinguish candidate distributions may fail, whereas an extended version of the Crémer-McLean auction simultaneously extracts full social surplus under each candidate distribution. With an algebraic argument, we give a tight bound on the number of samples needed by this auction, which is the difference between the number of candidate distributions and the dimension of the linear space they span.

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Supply-limiting mechanisms

Cited by 42 publications

References 26 publications

The sample complexity of revenue maximization

The sample complexity of revenue maximization

Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

Optimal auctions for correlated buyers with sampling

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