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The Competition Complexity of Auctions: A Bulow-Klemperer Result for Multi-Dimensional Bidders

Published: 20 June 2017 Publication History

Abstract

A seminal result of Bulow and Klemperer [1989] demonstrates the power of competition for extracting revenue: when selling a single item to n bidders whose values are drawn i.i.d. from a regular distribution, the simple welfare-maximizing VCG mechanism (in this case, a second price-auction) with one additional bidder extracts at least as much revenue in expectation as the optimal mechanism. The beauty of this theorem stems from the fact that VCG is a prior-independent mechanism, where the seller possesses no information about the distribution, and yet, by recruiting one additional bidder it performs better than any prior-dependent mechanism tailored exactly to the distribution at hand (without the additional bidder).
In this work, we establish the first full Bulow-Klemperer results in multi-dimensional environments, proving that by recruiting additional bidders, the revenue of the VCG mechanism surpasses that of the optimal (possibly randomized, Bayesian incentive compatible) mechanism. For a given environment with i.i.d. bidders, we term the number of additional bidders needed to achieve this guarantee the environment's competition complexity.
Using the recent duality-based framework of Cai et al. [2016] for reasoning about optimal revenue, we show that the competition complexity of n bidders with additive valuations over m independent, regular items is at most n+2m-2 and at least log(m). We extend our results to bidders with additive valuations subject to downward-closed constraints, showing that these significantly more general valuations increase the competition complexity by at most an additive m-1 factor. We further improve this bound for the special case of matroid constraints, and provide additional extensions as well.

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  • (2024)Settling the Competition Complexity of Additive Buyers over Independent ItemsProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673627(420-446)Online publication date: 8-Jul-2024
  • (2024)The Power of Two-Sided Recruitment in Two-Sided MarketsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649669(201-212)Online publication date: 10-Jun-2024
  • (2024)Benchmark-Tight Approximation Ratio of Simple Mechanism for a Unit-Demand Buyer2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00082(1251-1259)Online publication date: 27-Oct-2024
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cover image ACM Conferences
EC '17: Proceedings of the 2017 ACM Conference on Economics and Computation
June 2017
740 pages
ISBN:9781450345279
DOI:10.1145/3033274
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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New York, NY, United States

Publication History

Published: 20 June 2017

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Author Tags

  1. prior-independence
  2. revenue maximization
  3. simple auctions

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EC '17
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EC '17: ACM Conference on Economics and Computation
June 26 - 30, 2017
Massachusetts, Cambridge, USA

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EC '17 Paper Acceptance Rate 75 of 257 submissions, 29%;
Overall Acceptance Rate 664 of 2,389 submissions, 28%

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The 25th ACM Conference on Economics and Computation
July 7 - 11, 2025
Stanford , CA , USA

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Cited By

View all
  • (2024)Settling the Competition Complexity of Additive Buyers over Independent ItemsProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673627(420-446)Online publication date: 8-Jul-2024
  • (2024)The Power of Two-Sided Recruitment in Two-Sided MarketsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649669(201-212)Online publication date: 10-Jun-2024
  • (2024)Benchmark-Tight Approximation Ratio of Simple Mechanism for a Unit-Demand Buyer2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00082(1251-1259)Online publication date: 27-Oct-2024
  • (2024)Multi-objective Mechanism Design via AI-Driven ApproachesAI-Driven Mechanism Design10.1007/978-981-97-9286-3_4(95-127)Online publication date: 30-Sep-2024
  • (2022)Maximizing revenue under market shrinkage and market uncertaintyProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3600390(1643-1655)Online publication date: 28-Nov-2022
  • (2022)Truthful facility assignment with resource augmentation: an exact analysis of serial dictatorshipMathematical Programming10.1007/s10107-022-01902-8203:1-2(901-930)Online publication date: 2-Nov-2022
  • (2021)99% Revenue with Constant Enhanced CompetitionProceedings of the 22nd ACM Conference on Economics and Computation10.1145/3465456.3467647(224-241)Online publication date: 18-Jul-2021
  • (2021)Simple Economies are Almost OptimalProceedings of the 22nd ACM Conference on Economics and Computation10.1145/3465456.3467563(134-135)Online publication date: 18-Jul-2021
  • (2021)The randomized communication complexity of randomized auctionsProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451111(882-895)Online publication date: 15-Jun-2021
  • (2021)Risk-Robust Mechanism Design for a Prospect-Theoretic BuyerTheory of Computing Systems10.1007/s00224-021-10054-966:3(616-644)Online publication date: 2-Aug-2021
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