IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/2065.html
   My bibliography  Save this paper

Informationally Robust Optimal Auction Design

Author

Listed:

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," Cowles Foundation Discussion Papers 2065, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2065
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d20/d2065.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nenad Kos & Matthias Messner, 2015. "Selling to the Mean," CESifo Working Paper Series 5443, CESifo.
    2. Hansen, Lars-Peter & Sargent, Thomas-J, 2001. "Acknowledgement Misspecification in Macroeconomic Theory," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(S1), pages 213-227, February.
    3. 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..
    4. 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..
    5. 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.
    6. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    9. 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.
    10. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    11. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-361, March.
    12. Lars Peter Hansen & Thomas J. Sargent, 2001. "Acknowledging Misspecification in Macroeconomic Theory," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 519-535, July.
    13. 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. 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.

    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. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2022.
    2. Wanchang Zhang, 2022. "Auctioning Multiple Goods without Priors," Papers 2204.13726, arXiv.org.
    3. Song, Yangwei, 2018. "Efficient Implementation with Interdependent Valuations and Maxmin Agents," Rationality and Competition Discussion Paper Series 92, CRC TRR 190 Rationality and Competition.
    4. Song, Yangwei, 2022. "Approximate Bayesian Implementation and Exact Maxmin Implementation: An Equivalence," Rationality and Competition Discussion Paper Series 362, CRC TRR 190 Rationality and Competition.
    5. 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.
    6. Ronald M. Harstad, 2005. "Rational Participation Revolutionizes Auction Theory," Working Papers 0518, Department of Economics, University of Missouri.
    7. Hyoung-Goo Kang & Richard M. Burton & Will Mitchell, 2021. "How firm boundaries and relatedness jointly affect diversification value: trade-offs between governance and flexibility," Computational and Mathematical Organization Theory, Springer, vol. 27(1), pages 1-34, March.
    8. Vlad Mares & Ronald Harstad, 2007. "Ex-post full surplus extraction, straightforwardly," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 399-410, August.
    9. Song, Yangwei, 2023. "Approximate Bayesian implementation and exact maxmin implementation: An equivalence," Games and Economic Behavior, Elsevier, vol. 139(C), pages 56-87.
    10. Fernando Branco, 1996. "Common value auctions with independent types," Review of Economic Design, Springer;Society for Economic Design, vol. 2(1), pages 283-309, December.
    11. Wanchang Zhang, 2022. "Information-Robust Optimal Auctions," Papers 2205.04137, arXiv.org.
    12. Song, Yangwei, 2018. "Efficient implementation with interdependent valuations and maxmin agents," Journal of Economic Theory, Elsevier, vol. 176(C), pages 693-726.
    13. Martin Szydlowski, 2012. "Ambiguity in Dynamic Contracts," Discussion Papers 1543, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. 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.
    15. 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..
    16. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    17. Claude d'Aspremont & Jacques Crémer & Louis-André Gérard-Varet, 2003. "Correlation, independence, and Bayesian incentives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 281-310, October.
    18. Nenad Kos & Matthias Messner, 2015. "Selling to the mean," Working Papers 551, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    19. Brock, W. A. & Xepapadeas, A., 2015. "Modeling Coupled Climate, Ecosystems, and Economic Systems," Climate Change and Sustainable Development 206837, Fondazione Eni Enrico Mattei (FEEM).
    20. Anja Prummer, "undated". "Discrimination in Promotion," Working Papers 905, Queen Mary University of London, School of Economics and Finance.

    More about this item

    Keywords

    Optimal auctions; common values; information structure; model 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cwl:cwldpp:2065. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.