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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
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