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Optimal Auction Design With Common Values: An Informationally Robust Approach

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  • 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.

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  • 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
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    References listed on IDEAS

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    Cited by:

    1. Alexander Teytelboym & Shengwu Li & Scott Duke Kominers & Mohammad Akbarpour & Piotr Dworczak, 2021. "Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(3), pages 709-750, July.
    2. Dirk Bergemann & Tibor Heumann & Stephen Morris, 2022. "Screening with Persuasion," Papers 2212.03360, arXiv.org.
    3. Larionov, Daniil & Pham, Hien & Yamashita, Takuro & Zhu, Shuguang, 2021. "First Best Implementation with Costly Information Acquisition," TSE Working Papers 21-1261, Toulouse School of Economics (TSE), revised Apr 2022.
    4. Eitan Sapiro-Gheiler, 2021. "Persuasion with Ambiguous Receiver Preferences," Papers 2109.11536, arXiv.org, revised Aug 2023.
    5. Piotr Dworczak & Alessandro Pavan, 2022. "Preparing for the Worst but Hoping for the Best: Robust (Bayesian) Persuasion," Econometrica, Econometric Society, vol. 90(5), pages 2017-2051, September.
    6. Chen, Yi-Chun & Yang, Xiangqian, 2023. "Information design in optimal auctions," Journal of Economic Theory, Elsevier, vol. 212(C).
    7. Dirk Bergemann & Tan Gan & Yingkai Li, 2023. "Managing Persuasion Robustly: The Optimality of Quota Rules," Papers 2310.10024, arXiv.org.
    8. Pathikrit Basu, 2023. "Mechanism design with model specification," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 263-276, August.
    9. Kevin He & Fedor Sandomirskiy & Omer Tamuz, 2021. "Private Private Information," Papers 2112.14356, arXiv.org, revised Jun 2023.
    10. Tommaso Denti & Doron Ravid, 2023. "Robust Predictions in Games with Rational Inattention," Papers 2306.09964, arXiv.org.
    11. Yi-Chun Chen & Gaoji Hu & Xiangqian Yang, 2022. "Information Design in Allocation with Costly Verification," Papers 2210.16001, arXiv.org.
    12. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.
    13. Dirk Bergemann & Tibor Heumann & Stephen Morris, 2023. "Bidder-Optimal Information Structures in Auctions," Cowles Foundation Discussion Papers 2375, Cowles Foundation for Research in Economics, Yale University.
    14. Stefan Seifert & Silke Hüttel, 2023. "Is there a risk of a winner’s curse in farmland auctions?," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 50(3), pages 1140-1177.
    15. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    16. Jinsoo Bae & John H. Kagel, 2022. "Selling shares to budget-constrained bidders: an experimental study of the proportional auction," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 8(1), pages 45-55, December.
    17. Wanchang Zhang, 2022. "Robust Private Supply of a Public Good," Papers 2201.00923, arXiv.org, revised Jan 2022.
    18. Longjian Li, 2022. "Ambiguous Cheap Talk," Papers 2209.08494, arXiv.org.
    19. Xu Lang, 2023. "A Belief-Based Characterization of Reduced-Form Auctions," Papers 2307.04070, arXiv.org.
    20. Wanchang Zhang, 2022. "Auctioning Multiple Goods without Priors," Papers 2204.13726, arXiv.org.
    21. Wanchang Zhang, 2022. "Information-Robust Optimal Auctions," Papers 2205.04137, arXiv.org.

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