99% Revenue via Enhanced Competition

Feldman, Michal; Friedler, Ophir; Rubinstein, Aviad

doi:10.1145/3219166.3219202

Cited by 15 publications

(31 citation statements)

References 35 publications

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“…Our main result essentially achieves the greatly improved bound of [FFR18] (and improves it further) without losing any revenue: we prove a competition complexity bound of n(2 + ln(1 + m/n)). This guarantee is tight up to constant factors (and remains tight even if one is willing to lose an ε fraction), due to a lower bound of [FFR18].…”

Section: Connection To Related Workmentioning

confidence: 62%

“…The two works most directly related to ours are [EFF + 17a] and [FFR18]. The one-sentence distinction between our results and these is that we strictly improve their main results regarding selling separately to additive bidders with independent items, but do not address alternative settings.…”

Section: Connection To Related Workmentioning

confidence: 74%

“…Feldman et al [FFR18] prove that selling separately to O(n ln(m/n)/ε) additional buyers exceeds a (1 − ε) fraction of the optimal revenue (without the additional buyers). Our main result essentially achieves the greatly improved bound of [FFR18] (and improves it further) without losing any revenue: we prove a competition complexity bound of n(2 + ln(1 + m/n)). This guarantee is tight up to constant factors (and remains tight even if one is willing to lose an ε fraction), due to a lower bound of [FFR18].…”

Section: Connection To Related Workmentioning

confidence: 99%

“…"Big n Regime": For n additive bidders with m = o(n) independent items, Eden et al [EFF + 17a] prove a competition complexity bound of n + 2(m − 1). Feldman et al [FFR18] prove that for any ε, there exists a constant δ(ε) such that if n ≥ m/δ(ε), selling separately (without any additional bidders) achieves a (1 − ε) fraction of the optimal revenue. Our main result improves the guarantee of [EFF + 17a] to 9 √ nm and also implies the result of [FFR18] (with δ(ε) = ε 2 /81).…”

Section: Connection To Related Workmentioning

confidence: 99%

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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: 62%

Section: Connection To Related Workmentioning

confidence: 74%

Section: Connection To Related Workmentioning

confidence: 99%

Section: Connection To Related Workmentioning

confidence: 99%

See 2 more Smart Citations

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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“…Roughgarden et al [16] showed a Bulow-Klemperer type result for matching environments. Eden et al [7] and Feldman et al [8] studied, for auctions selling multiple heterogenous items, the number of duplicate bidders needed for the VCG auction's revenue to approximate the optimal without duplicates. The bidders' preferences are i.i.d.…”

Section: Introductionmentioning

confidence: 99%

The Vickrey Auction with a Single Duplicate Bidder Approximates the Optimal Revenue

Liaw

Randhawa

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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Bulow and Klemperer's well-known result states that, in a single-item auction where the n bidders' values are independently and identically drawn from a regular distribution, the Vickrey auction with one additional bidder (a duplicate) extracts at least as much revenue as the optimal auction without the duplicate. Hartline and Roughgarden, in their influential 2009 paper, removed the requirement that the distributions be identical, at the cost of allowing the Vickrey auction to recruit n duplicates, one from each distribution, and relaxing its revenue advantage to a 2approximation.In this work we restore Bulow and Klemperer's number of duplicates in Hartline and Roughgarden's more general setting with a worse approximation ratio. We show that recruiting a duplicate from one of the distributions suffices for the Vickrey auction to 10-approximate the optimal revenue. We also show that in a k-items unit demand auction, recruiting k duplicates suffices for the VCG auction to O(1)-approximate the optimal revenue.As another result, we tighten the analysis for Hartline and Roughgarden's Vickrey auction with n duplicates for the case with two bidders in the auction. We show that in this case the Vickrey auction with two duplicates obtains at least 3/4 of the optimal revenue. This is tight by meeting a lower bound by Hartline and Roughgarden. En route, we obtain a transparent analysis of their 2-approximation for n bidders, via a natural connection to Ronen's lookahead auction.

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On the Competition Complexity of Dynamic Mechanism Design

Liu

Psomas

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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The Competition Complexity of an auction measures how much competition is needed for the revenue of a simple auction to surpass the optimal revenue. A classic result from auction theory by Bulow and Klemperer [11], states that the Competition Complexity of VCG, in the case of n i.i.d. buyers and a single item, is 1. In other words, it is better to invest in recruiting one extra buyer and run a second price auction than to invest in learning exactly the buyers' underlying distribution and run the revenuemaximizing auction tailored to this distribution.In this paper we study the Competition Complexity of dynamic auctions. Consider the following problem: a monopolist is auctioning off m items in m consecutive stages to n interested buyers. A buyer realizes her value for item k in the beginning of stage k. How many additional buyers are necessary and sufficient for a second price auction at each stage to extract revenue at least that of the optimal dynamic auction?We prove that the Competition Complexity of dynamic auctions is at most 3n -and at least linear in n -even when the buyers' values are correlated across stages, under a monotone hazard rate assumption on the stage (marginal) distributions. This assumption can be relaxed if one settles for independent stages. We also prove results on the number of additional buyers necessary for VCG at every stage to be an α-approximation of the optimal revenue; we term this number the α-approximate Competition Complexity. For example, under the same mild assumptions on the stage distributions we prove that one extra buyer suffices for a 1 e -approximation. As a corollary we provide the first results on prior-independent dynamic auctions. This is, to the best of our knowledge, the first nontrivial positive guarantees for simple ex-post IR dynamic auctions for correlated stages.A key step towards proving bounds on the Competition Complexity is getting a good benchmark/upper bound to the optimal revenue. To this end, we extend the recent duality framework of [14] to dynamic settings. As an aside to our approach we obtain a revenue non-monotonicity lemma for dynamic auctions, which may be of independent interest.

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99% Revenue via Enhanced Competition

Cited by 15 publications

References 35 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

The Vickrey Auction with a Single Duplicate Bidder Approximates the Optimal Revenue

On the Competition Complexity of Dynamic Mechanism Design

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