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Informationally Robust Optimal Auction Design

Author

Listed:
  • Dirk Bergemann

    (Yale University)

  • Benjamin Brooks

    (University of Chicago)

  • Stephen Morris

    (Princeton University)

Abstract

A single unit of a good is to be sold by auction to one of two buyers. The good has either a high value or a low value, with known prior probabilities. The designer of the auction knows the prior over values but is uncertain about the correct model of the buyers' beliefs. The designer evaluates a given auction design by the lowest expected revenue that would be generated across all models of buyers' information that are consistent with the common prior and across all Bayesian equilibria. An optimal auction for such a seller is constructed, as is a worst-case model of buyers' information. The theory generates upper bounds on the seller's optimal payoff for general many-player and common-value models.

Suggested Citation

  • Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Informationally Robust Optimal Auction Design," Working Papers 084_2016, Princeton University, Department of Economics, Econometric Research Program..
    • Handle: RePEc:pri:metric:084_2016
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    References listed on IDEAS

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    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    2. 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.
    3. Fu, Hu & Haghpanah, Nima & Hartline, Jason & Kleinberg, Robert, 2021. "Full surplus extraction from samples," Journal of Economic Theory, Elsevier, vol. 193(C).
    4. Yi-Chun Chen & Xiangqian Yang, 2020. "Information Design in Optimal Auctions," Papers 2010.08990, arXiv.org, revised Oct 2022.
    5. Chen, Yi-Chun & Yang, Xiangqian, 2023. "Information design in optimal auctions," Journal of Economic Theory, Elsevier, vol. 212(C).
    6. Carl Heese & Stephan Lauermann, 2019. "Persuasion and Information Aggregation in Large Elections," CRC TR 224 Discussion Paper Series crctr224_2019_128, University of Bonn and University of Mannheim, Germany.
    7. Carl Heese & Stephan Lauermann, 2021. "Persuasion and Information Aggregation in Elections," ECONtribute Discussion Papers Series 112, University of Bonn and University of Cologne, Germany.
    8. Wanchang Zhang, 2021. "Correlation-Robust Optimal Auctions," Papers 2105.04697, arXiv.org, revised May 2022.
    9. 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.
    10. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    11. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.
    12. 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.
    13. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2022.
    14. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2019. "Revenue Guarantee Equivalence," American Economic Review, American Economic Association, vol. 109(5), pages 1911-1929, May.
    15. 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.
    16. 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.
    17. Amine Allouah & Omar Besbes, 2020. "Prior-Independent Optimal Auctions," Management Science, INFORMS, vol. 66(10), pages 4417-4432, October.
    18. 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.
    19. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    20. Wanchang Zhang, 2022. "Robust Private Supply of a Public Good," Papers 2201.00923, arXiv.org, revised Jan 2022.
    21. Ethan Che, 2019. "Distributionally Robust Optimal Auction Design under Mean Constraints," Papers 1911.07103, arXiv.org, revised Feb 2022.

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    More about this item

    Keywords

    Optimal auctions; common values; information structure; mo del uncertainty; ambiguity aversion; robustness; Bayes correlated equilibrium; revenue maximization; revenue equivalence; information rent;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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