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Auction design with ambiguity: Optimality of the first-price auction

Author

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  • Hwang, Sung-Ha
  • Koh, Youngwoo
  • Baik, Sosung

Abstract

We study the optimal auction design problem when bidders are ambiguity averse and follow the max-min expected utility model. Each bidder’s set of priors consists of beliefs that are close to the seller’s belief, where “closeness” is defined by a divergence. For a given allocation rule, we show that optimal transfers belong to a specific class of transfers, termed win-lose dependent transfers, in which bidders’ transfers upon winning and losing depend only on their own types but not on their opponents’ type reports. This result effectively reduces the infinite-dimensional problem of identifying an optimal transfer function into a two-dimensional problem of determining two constants-one for winning and another for losing. Solving this reduced problem, we show that among efficient mechanisms without transfers to losing bidders, the first-price auction is optimal, thereby outperforming other auction formats such as the second-price auction. We also discuss how the structure of the set of priors is related to the revenue ranking between the first- and second-price auctions.

Suggested Citation

  • Hwang, Sung-Ha & Koh, Youngwoo & Baik, Sosung, 2026. "Auction design with ambiguity: Optimality of the first-price auction," Games and Economic Behavior, Elsevier, vol. 157(C), pages 298-321.
    • Handle: RePEc:eee:gamebe:v:157:y:2026:i:c:p:298-321
    DOI: 10.1016/j.geb.2026.02.001
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    References listed on IDEAS

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    1. Sarah Auster & Christian Kellner, 2020. "Robust Bidding and Revenue in Descending Price Auctions," CRC TR 224 Discussion Paper Series crctr224_2020_146, University of Bonn and University of Mannheim, Germany.
    2. Auster, Sarah, 2018. "Robust contracting under common value uncertainty," Theoretical Economics, Econometric Society, vol. 13(1), January.
    3. Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    4. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.
    5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    6. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    7. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    8. Laohakunakorn, Krittanai & Levy, Gilat & Razin, Ronny, 2019. "Private and common value auctions with ambiguity over correlation," Journal of Economic Theory, Elsevier, vol. 184(C).
    9. Bodoh-Creed, Aaron L., 2012. "Ambiguous beliefs and mechanism design," Games and Economic Behavior, Elsevier, vol. 75(2), pages 518-537.
    10. John C. Duchi & Peter W. Glynn & Hongseok Namkoong, 2021. "Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 946-969, August.
    11. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    12. 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.
    13. , & , & ,, 2006. "Optimal auctions with ambiguity," Theoretical Economics, Econometric Society, vol. 1(4), pages 411-438, December.
    14. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    15. Kin Chung Lo, 1998. "Sealed bid auctions with uncertainty averse bidders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 1-20.
    16. Bose, Subir & Daripa, Arup, 2009. "A dynamic mechanism and surplus extraction under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2084-2114, September.
    17. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    19. Laohakunakorn, Krittanai & Levy, Gilat & Razin, Ronny, 2019. "Private and common value auctions with ambiguity over correlation," LSE Research Online Documents on Economics 101410, London School of Economics and Political Science, LSE Library.
    20. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    21. Kocherlakota, Narayana R. & Song, Yangwei, 2019. "Public goods with ambiguity in large economies," Journal of Economic Theory, Elsevier, vol. 182(C), pages 218-246.
    22. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    23. Wolitzky, Alexander, 2016. "Mechanism design with maxmin agents: theory and an application to bilateral trade," Theoretical Economics, Econometric Society, vol. 11(3), September.
    24. Steven Stong, 2018. "Ambiguity aversion in the all‐pay auction and war of attrition," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(6), pages 822-839, December.
    25. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
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    Keywords

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    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

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