IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v89y2021i3p1313-1360.html
   My bibliography  Save this article

Optimal Auction Design With Common Values: An Informationally Robust Approach

Author

Listed:
  • Benjamin Brooks
  • Songzi Du

Abstract

A profit‐maximizing seller has a single unit of a good to sell. The bidders have a pure common value that is drawn from a distribution that is commonly known. The seller does not know the bidders' beliefs about the value and thinks that beliefs are designed adversarially by Nature to minimize profit. We construct a strong maxmin solution to this joint mechanism design and information design problem, consisting of a mechanism, an information structure, and an equilibrium, such that neither the seller nor Nature can move profit in their respective preferred directions, even if the deviator can select the new equilibrium. The mechanism and information structure solve a family of maxmin mechanism design and minmax information design problems, regardless of how an equilibrium is selected. The maxmin mechanism takes the form of a proportional auction: each bidder submits a one‐dimensional bid, the aggregate allocation and aggregate payment depend on the aggregate bid, and individual allocations and payments are proportional to bids. We report a number of additional properties of the maxmin mechanisms, including what happens as the number of bidders grows large and robustness with respect to the prior over the value.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:3:p:1313-1360
    DOI: 10.3982/ECTA16297
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA16297
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA16297?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
    ---><---

    References listed on IDEAS

    as
    1. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-194, March.
    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. Chen, Yi-Chun & Li, Jiangtao, 2018. "Revisiting the foundations of dominant-strategy mechanisms," Journal of Economic Theory, Elsevier, vol. 178(C), pages 294-317.
    4. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    5. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    6. McAfee, R Preston & McMillan, John & Reny, Philip J, 1989. "Extracting the Surplus in the Common-Value Auction," Econometrica, Econometric Society, vol. 57(6), pages 1451-1459, 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. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    9. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    10. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    11. 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.
    12. Yamashita, Takuro, 2018. "Revenue guarantees in auctions with a (correlated) common prior and additional information," TSE Working Papers 18-937, Toulouse School of Economics (TSE).
    13. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    14. Takuro Yamashita, 2015. "Implementation in Weakly Undominated Strategies: Optimality of Second-Price Auction and Posted-Price Mechanism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 1223-1246.
    Full references (including those not matched with items on IDEAS)

    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. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    2. NAKADA, Satoshi & NITZAN, Shmuel & UI, Takashi & 宇井, 貴志, 2017. "Robust Voting under Uncertainty," Discussion paper series HIAS-E-60, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    3. Wanchang Zhang, 2022. "Robust Private Supply of a Public Good," Papers 2201.00923, arXiv.org, revised Jan 2022.
    4. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    5. Wei He & Jiangtao Li & Weijie Zhong, 2024. "Rank-Guaranteed Auctions," Papers 2408.12001, arXiv.org.
    6. Ethan Che, 2019. "Distributionally Robust Optimal Auction Design under Mean Constraints," Papers 1911.07103, arXiv.org, revised Feb 2022.
    7. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2024.
    8. Wanchang Zhang, 2022. "Auctioning Multiple Goods without Priors," Papers 2204.13726, arXiv.org.
    9. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Strategy-proof multi-object mechanism design: Ex-post revenue maximization with non-quasilinear preferences," Journal of Economic Theory, Elsevier, vol. 188(C).
    10. Suzdaltsev, Alex, 2022. "Distributionally robust pricing in independent private value auctions," Journal of Economic Theory, Elsevier, vol. 206(C).
    11. Wanchang Zhang, 2022. "Information-Robust Optimal Auctions," Papers 2205.04137, arXiv.org.
    12. Garrett, Daniel F., 2020. "Payoff Implications of Incentive Contracting," TSE Working Papers 20-1140, Toulouse School of Economics (TSE).
    13. Dominic Coey & Bradley Larsen & Kane Sweeney, 2019. "The bidder exclusion effect," RAND Journal of Economics, RAND Corporation, vol. 50(1), pages 93-120, March.
    14. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Mechanism design without quasilinearity," Theoretical Economics, Econometric Society, vol. 15(2), May.
    15. Jeremy Bulow & Paul Klemperer, 2007. "When are Auctions Best?," Economics Papers 2007-W03, Economics Group, Nuffield College, University of Oxford.
    16. Che,Y.-K. & Kim,J., 2001. "Know thy enemies : knowledge of rivals' types and its effect on auctions," Working papers 9, Wisconsin Madison - Social Systems.
    17. Nicholas C Bedard & Jacob K Goeree & Ningyi Sun, 2023. "Multivariate Majorization in Principal-Agents Models," Papers 2308.13804, arXiv.org.
    18. Jeremy Bulow & Paul Klemperer, 2009. "Why Do Sellers (Usually) Prefer Auctions?," American Economic Review, American Economic Association, vol. 99(4), pages 1544-1575, September.
    19. Anton Kolotilin & Tymofiy Mylovanov & Andriy Zapechelnyuk & Ming Li, 2017. "Persuasion of a Privately Informed Receiver," Econometrica, Econometric Society, vol. 85(6), pages 1949-1964, November.
    20. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.

    More about this item

    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:wly:emetrp:v:89:y:2021:i:3:p:1313-1360. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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.