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Distributionally Robust Optimal Auction Design under Mean Constraints

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  • Ethan Che

Abstract

We study a seller who sells a single good to multiple bidders with uncertainty over the joint distribution of bidders' valuations, as well as bidders' higher-order beliefs about their opponents. The seller only knows the (possibly asymmetric) means of the marginal distributions of each bidder's valuation and the range. An adversarial nature chooses the worst-case distribution within this ambiguity set along with the worst-case information structure. We find that a second-price auction with a symmetric, random reserve price obtains the optimal revenue guarantee within a broad class of mechanisms we refer to as competitive mechanisms, which include standard auction formats, including the first-price auction, with or without reserve prices. The optimal mechanism possesses two notable characteristics. First, the mechanism treats all bidders identically even in the presence of ex-ante asymmetries. Second, when bidders are identical and the number of bidders $n$ grows large, the seller's optimal reserve price converges in probability to a non-binding reserve price and the revenue guarantee converges to the best possible revenue guarantee at rate $O(1/n)$.

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  • Ethan Che, 2019. "Distributionally Robust Optimal Auction Design under Mean Constraints," Papers 1911.07103, arXiv.org, revised Feb 2022.
    • Handle: RePEc:arx:papers:1911.07103
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    References listed on IDEAS

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    Cited by:

    1. Wanchang Zhang, 2022. "Robust Private Supply of a Public Good," Papers 2201.00923, arXiv.org, revised Jan 2022.
    2. Chen, Yi-Chun & Yang, Xiangqian, 2023. "Information design in optimal auctions," Journal of Economic Theory, Elsevier, vol. 212(C).
    3. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    4. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.
    5. Wanchang Zhang, 2021. "Correlation-Robust Optimal Auctions," Papers 2105.04697, arXiv.org, revised May 2022.
    6. Jerry Anunrojwong & Santiago R. Balseiro & Omar Besbes, 2023. "Robust Auction Design with Support Information," Papers 2305.09065, arXiv.org, revised Aug 2023.

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