IDEAS home Printed from https://ideas.repec.org/p/bon/boncrc/crctr224_2018_031.html

A Theory of Auctions With Endogenous Valuations

Author

Listed:
  • Benny Moldovanu

  • Alex Gershkov

  • Philipp Strack

Abstract

We study the revenue maximizing allocation of m units among n symmetric agents that have unit demand and convex preferences over the probability of receiving an object. Such preferences are naturally induced by a game where the agents take costly actions that affect their values before participating in the mechanism. Both the uniform m + 1 price auction and the discriminatory pay-your-bid auction with reserve prices constitute symmetric revenue maximizing mechanisms. Contrasting the case with linear preferences, the optimal reserve price reacts to both demand and supply, i.e., it depends both on the number of objects m and on number of agents n. The main tool in our analysis is an integral inequality involving majorization, super-modularity and convexity due to Fan and Lorentz (1954).

Suggested Citation

  • Benny Moldovanu & Alex Gershkov & Philipp Strack, 2018. "A Theory of Auctions With Endogenous Valuations," CRC TR 224 Discussion Paper Series crctr224_2018_031, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2018_031
    as

    Download full text from publisher

    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp031
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Ce Li & Qianfan Zhang & Weiqiang Zheng, 2025. "From Best Responses to Learning: Investment Efficiency in Dynamic Environment," Papers 2511.01157, arXiv.org.
    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. 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.
    5. Zihao Li, 2025. "Coasian Dynamics with Set-Valued Allocative Efficiency: Information Goods," Papers 2507.13137, arXiv.org, revised Jan 2026.
    6. 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.
    7. 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.
    8. Frank Yang & Kai Hao Yang, 2025. "Multidimensional Monotonicity and Economic Applications," Cowles Foundation Discussion Papers 2428, Cowles Foundation for Research in Economics, Yale University.
    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

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

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

    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:bon:boncrc:crctr224_2018_031. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: CRC Office (email available below). General contact details of provider: https://www.crctr224.de .

    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.