IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v73y2025i3p1307-1319.html
   My bibliography  Save this article

Revenue Maximization Under Unknown Private Values with Nonobligatory Inspection

Author

Listed:
  • Saeed Alaei

    (Google Research, Mountain View, California 94043)

  • Ali Makhdoumi

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Azarakhsh Malekian

    (Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

Abstract

We consider the problem of selling k units of an item to n unit-demand buyers to maximize revenue, where the buyers’ values are independently distributed (not necessarily identical) according to publicly known distributions but unknown to the buyers themselves, with the option of allowing buyers to inspect the item at a cost. This problem can be interpreted as a revenue-maximizing variant of Weitzman’s Pandora’s problem with a nonobligatory inspection. We first fully characterize the optimal mechanism in selling to a single buyer subject to an upper bound on the allocation probability. Using this characterization, we then present an approximation mechanism that achieves 1 − 1 / k + 3 of the optimal revenue in expectation. Our mechanism is sequential and has a simple implementation that works in an online setting where buyers arrive in an arbitrary unknown order, yet achieving the aforementioned approximation with respect to the optimal offline mechanism.

Suggested Citation

  • Saeed Alaei & Ali Makhdoumi & Azarakhsh Malekian, 2025. "Revenue Maximization Under Unknown Private Values with Nonobligatory Inspection," Operations Research, INFORMS, vol. 73(3), pages 1307-1319, May.
  • Handle: RePEc:inm:oropre:v:73:y:2025:i:3:p:1307-1319
    DOI: 10.1287/opre.2022.0024
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2022.0024
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.2022.0024?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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:inm:oropre:v:73:y:2025:i:3:p:1307-1319. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.