IDEAS home Printed from https://ideas.repec.org/a/the/publsh/4555.html
   My bibliography  Save this article

Worst-case equilibria in first-price auctions

Author

Listed:
  • Gretschko, Vitali

    (University of Mannheim, Deparment of Economics)

  • Mass, Helene

    (University of Bonn, Institute for Microeconomics)

Abstract

The usual analysis of bidding in first-price auctions assumes that bidders know the distribution of valuations. We analyze first-price auctions in which bidders do not know the precise distribution of their competitors' valuations, but only the mean of the distribution. We propose a novel equilibrium solution concept based on worst-case reasoning. We find an essentially unique and efficient worst-case equilibrium of the first-price auction, which has appealing properties from both the bidders' and the seller's point of view.

Suggested Citation

  • Gretschko, Vitali & Mass, Helene, 2024. "Worst-case equilibria in first-price auctions," Theoretical Economics, Econometric Society, vol. 19(1), January.
    • Handle: RePEc:the:publsh:4555
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20240061/38402/1160
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tristan Gagnon-Bartsch & Marco Pagnozzi & Antonio Rosato, 2021. "Projection of Private Values in Auctions," American Economic Review, American Economic Association, vol. 111(10), pages 3256-3298, October.
    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. Ignacio Esponda, 2008. "Information feedback in first price auctions," RAND Journal of Economics, RAND Corporation, vol. 39(2), pages 491-508, June.
    4. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    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. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.
    7. 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.
    8. Riley, John G, 1989. "Expected Revenue from Open and Sealed Bid Auctions," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 41-50, Summer.
    9. Bodoh-Creed, Aaron L., 2012. "Ambiguous beliefs and mechanism design," Games and Economic Behavior, Elsevier, vol. 75(2), pages 518-537.
    10. Amine Allouah & Omar Besbes, 2020. "Prior-Independent Optimal Auctions," Management Science, INFORMS, vol. 66(10), pages 4417-4432, October.
    11. Gabriel Carroll, 2015. "Robustness and Linear Contracts," American Economic Review, American Economic Association, vol. 105(2), pages 536-563, February.
    12. Helene Mass, 2020. "Strategies Under Strategic Uncertainty," CRC TR 224 Discussion Paper Series crctr224_2020_157, University of Bonn and University of Mannheim, Germany.
    13. Alessandro Chiesa & Silvio Micali & Zeyuan Allen Zhu, 2015. "Knightian Analysis of the Vickrey Mechanism," Econometrica, Econometric Society, vol. 83(5), pages 1727-1754, September.
    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. Joseph Feffer, 2024. "Scoring Auctions with Coarse Beliefs," Papers 2410.06150, 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. Ju Hu & Xi Weng, 2021. "Robust persuasion of a privately informed receiver," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 909-953, October.
    3. Suzdaltsev, Alex, 2022. "Distributionally robust pricing in independent private value auctions," Journal of Economic Theory, Elsevier, vol. 206(C).
    4. Pieter Kleer & Johan van Leeuwaarden, 2022. "Optimal Stopping Theory for a Distributionally Robust Seller," Papers 2206.02477, arXiv.org, revised Jun 2022.
    5. Gretschko, Vitali & Mass, Helene, 2018. "Endogenous worst-case beliefs in first-price auctions," ZEW Discussion Papers 18-056, ZEW - Leibniz Centre for European Economic Research.
    6. Shixin Wang, 2023. "The Power of Simple Menus in Robust Selling Mechanisms," Papers 2310.17392, arXiv.org, revised Sep 2024.
    7. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2024.
    8. Shixin Wang, 2024. "Semi-Separable Mechanisms in Multi-Item Robust Screening," Papers 2408.13580, arXiv.org.
    9. 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.
    10. Giuseppe Lopomo & Luca Rigotti & Chris Shannon, 2021. "Uncertainty in Mechanism Design," Papers 2108.12633, arXiv.org.
    11. Shaowei Ke & Qi Zhang, 2020. "Randomization and Ambiguity Aversion," Econometrica, Econometric Society, vol. 88(3), pages 1159-1195, May.
    12. Çağıl Koçyiğit & Daniel Kuhn & Napat Rujeerapaiboon, 2024. "Regret Minimization and Separation in Multi-Bidder, Multi-Item Auctions," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1543-1561, December.
    13. Ethan Che, 2019. "Distributionally Robust Optimal Auction Design under Mean Constraints," Papers 1911.07103, arXiv.org, revised Feb 2022.
    14. Nenad Kos & Matthias Messner, 2015. "Selling to the mean," Working Papers 551, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    15. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    16. Vinicius Carrasco & Vitor Farinha Luz & Paulo K. Monteiro & Humberto Moreira, 2019. "Robust mechanisms: the curvature case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 203-222, July.
    17. Amine Allouah & Omar Besbes, 2020. "Prior-Independent Optimal Auctions," Management Science, INFORMS, vol. 66(10), pages 4417-4432, October.
    18. Wanchang Zhang, 2022. "Auctioning Multiple Goods without Priors," Papers 2204.13726, arXiv.org.
    19. 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.
    20. Zhaolin Li & Samuel N. Kirshner, 2021. "Salesforce Compensation and Two‐Sided Ambiguity: Robust Moral Hazard with Moment Information," Production and Operations Management, Production and Operations Management Society, vol. 30(9), pages 2944-2961, September.

    More about this item

    Keywords

    Auctions; subjective-belief equilibria; uncertainty;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:the:publsh:4555. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    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.