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Nontruthful Position Auctions Are More Robust to Misspecification

Author

Listed:
  • Paul Dütting

    (Google Research, Zurich 8002, Switzerland)

  • Felix Fischer

    (School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom)

  • David C. Parkes

    (John A. Paulson School of Engineering and Applied Sciences, Harvard University, Boston, Massachusetts 02134)

Abstract

We consider the classical model of sponsored search due to Edelman et al. and Varian and examine how robust standard position auctions are to a misspecification of the position-dependent quality factors used by this model. We show that under both complete and incomplete information a nontruthful position auction admits an efficient equilibrium for a strictly broader range of parameter values than the Vickrey-Clarke-Groves (VCG) mechanism, which would be truthful if the parameters were specified correctly. Our result for complete information concerns the generalized second-price (GSP) mechanism and is driven by a detailed understanding of the Nash equilibrium polytopes of the VCG mechanism and the GSP mechanism. Our result for incomplete information concerns the generalized first-price (GFP) mechanism and uses a surprising connection between the unique candidate equilibrium bidding functions of the VCG mechanism and the GFP mechanism.

Suggested Citation

  • Paul Dütting & Felix Fischer & David C. Parkes, 2024. "Nontruthful Position Auctions Are More Robust to Misspecification," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 901-927, May.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:2:p:901-927
    DOI: 10.1287/moor.2023.1380
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    References listed on IDEAS

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    1. 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.
    2. Paul Dütting & Felix Fischer & David C. Parkes, 2019. "Expressiveness and Robustness of First-Price Position Auctions," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 196-211, February.
    3. Hal R. Varian & Christopher Harris, 2014. "The VCG Auction in Theory and Practice," American Economic Review, American Economic Association, vol. 104(5), pages 442-445, May.
    4. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    5. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    6. Dütting, Paul & Fischer, Felix & Parkes, David C., 2019. "Expressiveness and robustness of first-price position auctions," LSE Research Online Documents on Economics 85877, London School of Economics and Political Science, LSE Library.
    7. Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 269-302, June.
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    Cited by:

    1. Dirk Bergemann & Marek Bojko & Paul DŸtting & Renato Paes Leme & Haifeng Xu & Song Zuo, 2024. "Data-Driven Mechanism Design: Jointly Eliciting Preferences and Information," Cowles Foundation Discussion Papers 2418, Cowles Foundation for Research in Economics, Yale University.

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