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Distributionally Robust Pricing in Independent Private Value Auctions

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  • Alex Suzdaltsev

Abstract

A seller chooses a reserve price in a second-price auction to maximize worst-case expected revenue when she knows only the mean of value distribution and an upper bound on either values themselves or variance. Values are private and iid. Using an indirect technique, we prove that it is always optimal to set the reserve price to the seller's own valuation. However, the maxmin reserve price may not be unique. If the number of bidders is sufficiently high, all prices below the seller's valuation, including zero, are also optimal. A second-price auction with the reserve equal to seller's value (or zero) is an asymptotically optimal mechanism (among all ex post individually rational mechanisms) as the number of bidders grows without bound.

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  • Alex Suzdaltsev, 2020. "Distributionally Robust Pricing in Independent Private Value Auctions," Papers 2008.01618, arXiv.org, revised Aug 2020.
    • Handle: RePEc:arx:papers:2008.01618
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    1. Kim-Sau Chung & J.C. Ely, 2007. "Foundations of Dominant-Strategy Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 447-476.
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    Cited by:

    1. Yi-Chun Chen & Xiangqian Yang, 2020. "Information Design in Optimal Auctions," Papers 2010.08990, arXiv.org, revised Oct 2022.
    2. Chen, Yi-Chun & Yang, Xiangqian, 2023. "Information design in optimal auctions," Journal of Economic Theory, Elsevier, vol. 212(C).
    3. Pieter Kleer & Johan van Leeuwaarden, 2022. "Optimal Stopping Theory for a Distributionally Robust Seller," Papers 2206.02477, arXiv.org, revised Jun 2022.
    4. Wanchang Zhang, 2022. "Information-Robust Optimal Auctions," Papers 2205.04137, arXiv.org.
    5. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).

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