IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v200y2022ics0022053121002209.html
   My bibliography  Save this article

Correlation-robust auction design

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053121002209
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2021.105403?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2017. "First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue," Econometrica, Econometric Society, vol. 85, pages 107-143, January.
    3. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    4. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
    5. Benjamin Brooks & Songzi Du, 2021. "Optimal Auction Design With Common Values: An Informationally Robust Approach," Econometrica, Econometric Society, vol. 89(3), pages 1313-1360, May.
    6. Tilman Börgers & Jiangtao Li, 2019. "Strategically Simple Mechanisms," Econometrica, Econometric Society, vol. 87(6), pages 2003-2035, November.
    7. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Informationally Robust Optimal Auction Design," Cowles Foundation Discussion Papers 2065, Cowles Foundation for Research in Economics, Yale University.
    8. Anne-Katrin Roesler & Balázs Szentes, 2017. "Buyer-Optimal Learning and Monopoly Pricing," American Economic Review, American Economic Association, vol. 107(7), pages 2072-2080, July.
    9. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.
    10. Alex Suzdaltsev, 2020. "Distributionally Robust Pricing in Independent Private Value Auctions," Papers 2008.01618, arXiv.org, revised Aug 2020.
    11. Songzi Du, 2018. "Robust Mechanisms Under Common Valuation," Econometrica, Econometric Society, vol. 86(5), pages 1569-1588, September.
    12. Alex Suzdaltsev, 2020. "An Optimal Distributionally Robust Auction," Papers 2006.05192, arXiv.org, revised Aug 2020.
    13. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2019. "Revenue Guarantee Equivalence," American Economic Review, American Economic Association, vol. 109(5), pages 1911-1929, May.
    14. Carrasco, Vinicius & Farinha Luz, Vitor & Kos, Nenad & Messner, Matthias & Monteiro, Paulo & Moreira, Humberto, 2018. "Optimal selling mechanisms under moment conditions," Journal of Economic Theory, Elsevier, vol. 177(C), pages 245-279.
    15. Jonathan Libgober & Xiaosheng Mu, 2021. "Informational Robustness in Intertemporal Pricing [Political Disagreement and Information in Elections]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(3), pages 1224-1252.
    16. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    17. Kevin Hasker & Robin Sickles, 2010. "eBay in the Economic Literature: Analysis of an Auction Marketplace," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 37(1), pages 3-42, August.
    18. Qingmin Liu & Konrad Mierendorff & Xianwen Shi & Weijie Zhong, 2019. "Auctions with Limited Commitment," American Economic Review, American Economic Association, vol. 109(3), pages 876-910, March.
    19. Chen, Yi-Chun & Li, Jiangtao, 2018. "Revisiting the foundations of dominant-strategy mechanisms," Journal of Economic Theory, Elsevier, vol. 178(C), pages 294-317.
    20. Wanchang Zhang, 2021. "Correlation-Robust Optimal Auctions," Papers 2105.04697, arXiv.org, revised May 2022.
    21. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    22. Gabriel Carroll, 2019. "Robustness in Mechanism Design and Contracting," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 139-166, August.
    23. Gilat Levy & Ronny Razin, 2015. "Correlation Neglect, Voting Behavior, and Information Aggregation," American Economic Review, American Economic Association, vol. 105(4), pages 1634-1645, April.
    24. Neeman, Zvika, 2003. "The effectiveness of English auctions," Games and Economic Behavior, Elsevier, vol. 43(2), pages 214-238, May.
    25. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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 Dec 2022.
    2. Longjian Li, 2022. "Ambiguous Cheap Talk," Papers 2209.08494, arXiv.org.
    3. Wanchang Zhang, 2022. "Auctioning Multiple Goods without Priors," Papers 2204.13726, arXiv.org.
    4. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.
    5. Komal Malik, 2022. "Optimal Robust Mechanism in Bilateral Trading," Papers 2212.14367, arXiv.org.
    6. Pieter Kleer & Johan van Leeuwaarden, 2022. "Optimal Stopping Theory for a Distributionally Robust Seller," Papers 2206.02477, arXiv.org, revised Jun 2022.
    7. Wanchang Zhang, 2022. "Information-Robust Optimal Auctions," Papers 2205.04137, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    2. Wanchang Zhang, 2022. "Robust Private Supply of a Public Good," Papers 2201.00923, arXiv.org, revised Jan 2022.
    3. Suzdaltsev, Alex, 2022. "Distributionally robust pricing in independent private value auctions," Journal of Economic Theory, Elsevier, vol. 206(C).
    4. Wanchang Zhang, 2022. "Auctioning Multiple Goods without Priors," Papers 2204.13726, arXiv.org.
    5. Satoshi Nakada & Shmuel Nitzan & Takashi Ui, 2022. "Robust Voting under Uncertainty," Working Papers on Central Bank Communication 038, University of Tokyo, Graduate School of Economics.
    6. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2022.
    7. Chen, Yi-Chun & Yang, Xiangqian, 2023. "Information design in optimal auctions," Journal of Economic Theory, Elsevier, vol. 212(C).
    8. Wanchang Zhang, 2022. "Information-Robust Optimal Auctions," Papers 2205.04137, arXiv.org.
    9. Benjamin Brooks & Songzi Du, 2021. "Optimal Auction Design With Common Values: An Informationally Robust Approach," Econometrica, Econometric Society, vol. 89(3), pages 1313-1360, May.
    10. Amine Allouah & Omar Besbes, 2020. "Prior-Independent Optimal Auctions," Management Science, INFORMS, vol. 66(10), pages 4417-4432, October.
    11. Wanchang Zhang, 2021. "Correlation-Robust Optimal Auctions," Papers 2105.04697, arXiv.org, revised May 2022.
    12. Yi-Chun Chen & Xiangqian Yang, 2020. "Information Design in Optimal Auctions," Papers 2010.08990, arXiv.org, revised Oct 2022.
    13. Tang, Rui & Zhang, Mu, 2021. "Maxmin implementation," Journal of Economic Theory, Elsevier, vol. 194(C).
    14. Ethan Che, 2019. "Distributionally Robust Optimal Auction Design under Mean Constraints," Papers 1911.07103, arXiv.org, revised Feb 2022.
    15. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.
    16. Jonathan Libgober & Xiaosheng Mu, 2022. "Coasian Dynamics under Informational Robustness," Papers 2202.04616, arXiv.org, revised Jan 2023.
    17. Tilman Börgers, 2017. "(No) Foundations of dominant-strategy mechanisms: a comment on Chung and Ely (2007)," Review of Economic Design, Springer;Society for Economic Design, vol. 21(2), pages 73-82, June.
    18. Chen, Yi-Chun & Li, Jiangtao, 2018. "Revisiting the foundations of dominant-strategy mechanisms," Journal of Economic Theory, Elsevier, vol. 178(C), pages 294-317.
    19. 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.
    20. 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.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:200:y:2022:i:c:s0022053121002209. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.