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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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    1. Benjamin Edelman & Michael Schwarz, 2010. "Optimal Auction Design and Equilibrium Selection in Sponsored Search Auctions," Harvard Business School Working Papers 10-054, Harvard Business School.
    2. Benjamin Edelman & Michael Schwarz, 2010. "Optimal Auction Design and Equilibrium Selection in Sponsored Search Auctions," American Economic Review, American Economic Association, vol. 100(2), pages 597-602, May.
    3. AmirMahdi Ahmadinejad & Sina Dehghani & MohammadTaghi Hajiaghayi & Brendan Lucier & Hamid Mahini & Saeed Seddighin, 2019. "From Duels to Battlefields: Computing Equilibria of Blotto and Other Games," Management Science, INFORMS, vol. 44(4), pages 1304-1325, November.
    4. Benjamin Edelman & Michael Ostrovsky & Michael Schwarz, 2007. "Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords," American Economic Review, American Economic Association, vol. 97(1), pages 242-259, March.
    5. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    6. Santiago R. Balseiro & Jon Feldman & Vahab Mirrokni & S. Muthukrishnan, 2014. "Yield Optimization of Display Advertising with Ad Exchange," Management Science, INFORMS, vol. 60(12), pages 2886-2907, December.
    7. L. Elisa Celis & Gregory Lewis & Markus Mobius & Hamid Nazerzadeh, 2014. "Buy-It-Now or Take-a-Chance: Price Discrimination Through Randomized Auctions," Management Science, INFORMS, vol. 60(12), pages 2927-2948, December.
    8. Dhangwatnotai, Peerapong & Roughgarden, Tim & Yan, Qiqi, 2015. "Revenue maximization with a single sample," Games and Economic Behavior, Elsevier, vol. 91(C), pages 318-333.
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