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Correlation-robust auction design

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  • He, Wei
  • Li, Jiangtao

Abstract

We study the design of auctions when the auctioneer has limited statistical information about the joint distribution of the bidders' valuations. More specifically, we consider an auctioneer who has an estimate of the marginal distribution of a generic bidder's valuation but does not have reliable information about the correlation structure. We analyze the performance of mechanisms in terms of the revenue guarantee, that is, the greatest lower bound of revenue across all joint distributions that are consistent with the marginals. A simple auction format, the second-price auction with no reserve price, is shown to be asymptotically optimal, as the number of bidders goes to infinity. For markets with a finite number of bidders, we (1) solve for the robustly optimal reserve price that generates the highest revenue guarantee among all second-price auctions with deterministic reserve prices, and (2) show that a second-price auction with a random reserve price generates the highest revenue guarantee among all standard dominant-strategy mechanisms.

Suggested Citation

  • He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:jetheo:v:200:y:2022:i:c:s0022053121002209
    DOI: 10.1016/j.jet.2021.105403
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    Cited by:

    1. Halil .Ibrahim Bayrak & c{C}au{g}{i}l Koc{c}yiu{g}it & Daniel Kuhn & Mustafa c{C}elebi P{i}nar, 2022. "Distributionally Robust Optimal Allocation with Costly Verification," Papers 2211.15122, arXiv.org, revised Jun 2024.
    2. Wei He & Jiangtao Li & Weijie Zhong, 2024. "Rank-Guaranteed Auctions," Papers 2408.12001, arXiv.org.
    3. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.
    4. Benjamin Brooks & Songzi Du, 2024. "On the Structure of Informationally Robust Optimal Mechanisms," Econometrica, Econometric Society, vol. 92(5), pages 1391-1438, September.
    5. Longjian Li, 2022. "Ambiguous Cheap Talk," Papers 2209.08494, arXiv.org.
    6. Wanchang Zhang, 2022. "Auctioning Multiple Goods without Priors," Papers 2204.13726, arXiv.org.
    7. Komal Malik, 2022. "Optimal Robust Mechanism in Bilateral Trading," Papers 2212.14367, arXiv.org.
    8. Pieter Kleer & Johan van Leeuwaarden, 2022. "Optimal Stopping Theory for a Distributionally Robust Seller," Papers 2206.02477, arXiv.org, revised Jun 2022.
    9. Wanchang Zhang, 2022. "Information-Robust Optimal Auctions," Papers 2205.04137, arXiv.org.

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    More about this item

    Keywords

    Robust mechanism design; Correlation; Second-price auction; Low reserve price; Duality approach; Optimal transport;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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