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Linear Program-Based Approximation for Personalized Reserve Prices

Author

Listed:
  • Mahsa Derakhshan

    (Department of Computer Science, University of Maryland, College Park, Maryland 20742)

  • Negin Golrezaei

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Renato Paes Leme

    (Google Research, New York, New York 10011)

Abstract

We study the problem of computing data-driven personalized reserve prices in eager second price auctions without having any assumption on valuation distributions. Here, the input is a data set that contains the submitted bids of n buyers in a set of auctions, and the problem is to return personalized reserve prices r that maximize the revenue earned on these auctions by running eager second price auctions with reserve r . For this problem, which is known to be NP complete, we present a novel linear program (LP) formulation and a rounding procedure, which achieves a 0.684 approximation. This improves over the 1 2 -approximation algorithm from Roughgarden and Wang. We show that our analysis is tight for this rounding procedure. We also bound the integrality gap of the LP, which shows that it is impossible to design an algorithm that yields an approximation factor larger than 0.828 with respect to this LP.

Suggested Citation

  • Mahsa Derakhshan & Negin Golrezaei & Renato Paes Leme, 2022. "Linear Program-Based Approximation for Personalized Reserve Prices," Management Science, INFORMS, vol. 68(3), pages 1849-1864, March.
    • Handle: RePEc:inm:ormnsc:v:68:y:2022:i:3:p:1849-1864
    DOI: 10.1287/mnsc.2020.3897
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    References listed on IDEAS

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