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A Theory of Auctions with Endogenous Valuations

Author

Listed:
  • Alex Gershkov
  • Benny Moldovanu
  • Philipp Strack
  • Mengxi Zhang

Abstract

We derive the symmetric, revenue-maximizing allocation of several units among agents who take costly actions that influence their values. The problem is equivalent to a reduced-form model where agents have nonexpected utility. The uniform-price auction and the discriminatory pay-your-bid auction with reserve prices that react to both demand and supply constitute symmetric, optimal mechanisms. We also identify a condition under which the overall optimal mechanism is indeed symmetric and illustrate the structure of the optimal asymmetric mechanism when the condition fails. The main tool in our analysis is an integral inequality based on Fan and Lorentz (1954).

Suggested Citation

  • Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2021. "A Theory of Auctions with Endogenous Valuations," Journal of Political Economy, University of Chicago Press, vol. 129(4), pages 1011-1051.
    • Handle: RePEc:ucp:jpolec:doi:10.1086/712735
    DOI: 10.1086/712735
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    Cited by:

    1. Sunil Dutta & Qintao Fan, 2025. "Innovation incentives and competition for corporate resources," Review of Accounting Studies, Springer, vol. 30(3), pages 2635-2672, September.
    2. Frank Yang & Kai Hao Yang, 2025. "Multidimensional Monotonicity and Economic Applications," Cowles Foundation Discussion Papers 2428, Cowles Foundation for Research in Economics, Yale University.
    3. Frank Yang & Kai Hao Yang, 2025. "Multidimensional Monotonicity and Economic Applications," Cowles Foundation Discussion Papers 2428R1, Cowles Foundation for Research in Economics, Yale University.
    4. Zihao Li, 2025. "Coasian Dynamics with Set-Valued Allocative Efficiency: Information Goods," Papers 2507.13137, arXiv.org, revised Jan 2026.
    5. 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.
    6. Ce Li & Qianfan Zhang & Weiqiang Zheng, 2025. "From Best Responses to Learning: Investment Efficiency in Dynamic Environment," Papers 2511.01157, arXiv.org.
    7. Xu Lang, 2022. "Reduced-form budget allocation with multiple public alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 335-359, August.
    8. Wasser, Cédric & Zhang, Mengxi, 2023. "Differential treatment and the winner's effort in contests with incomplete information," Games and Economic Behavior, Elsevier, vol. 138(C), pages 90-111.
    9. Agastya, Murali & Feng, Xin & Lu, Jingfeng, 2023. "Auction design with shortlisting when value discovery is covert," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    10. Frank Yang & Kai Hao Yang, 2025. "Multidimensional Monotonicity and Economic Applications," Papers 2502.18876, arXiv.org, revised Aug 2025.

    More about this item

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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