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An Optimal Distributionally Robust Auction

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  • Alex Suzdaltsev

Abstract

An indivisible object may be sold to one of $n$ agents who know their valuations of the object. The seller would like to use a revenue-maximizing mechanism but her knowledge of the valuations' distribution is scarce: she knows only the means (which may be different) and an upper bound for valuations. Valuations may be correlated. Using a constructive approach based on duality, we prove that a mechanism that maximizes the worst-case expected revenue among all deterministic dominant-strategy incentive compatible, ex post individually rational mechanisms is such that the object should be awarded to the agent with the highest linear score provided it is nonnegative. Linear scores are bidder-specific linear functions of bids. The set of optimal mechanisms includes other mechanisms but all those have to be close to the optimal linear score auction in a certain sense. When means are high, all optimal mechanisms share the linearity property. Second-price auction without a reserve is an optimal mechanism when the number of symmetric bidders is sufficiently high.

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  • Alex Suzdaltsev, 2020. "An Optimal Distributionally Robust Auction," Papers 2006.05192, arXiv.org, revised Aug 2020.
    • Handle: RePEc:arx:papers:2006.05192
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    References listed on IDEAS

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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.
    2. Chaithanya Bandi & Dimitris Bertsimas, 2014. "Optimal Design for Multi-Item Auctions: A Robust Optimization Approach," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1012-1038, November.
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    5. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
    6. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    7. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
    8. Wolitzky, Alexander, 2016. "Mechanism design with maxmin agents: theory and an application to bilateral trade," Theoretical Economics, Econometric Society, vol. 11(3), September.
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    Cited by:

    1. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    2. 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 Dec 2022.
    3. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    4. Giuseppe Lopomo & Luca Rigotti & Chris Shannon, 2021. "Uncertainty in Mechanism Design," Papers 2108.12633, arXiv.org.
    5. Alexander V. Kolesnikov & Fedor Sandomirskiy & Aleh Tsyvinski & Alexander P. Zimin, 2022. "Beckmann's approach to multi-item multi-bidder auctions," Papers 2203.06837, arXiv.org, revised Sep 2022.
    6. Suzdaltsev, Alex, 2022. "Distributionally robust pricing in independent private value auctions," Journal of Economic Theory, Elsevier, vol. 206(C).

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