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A Game-Theoretic Analysis of the Empirical Revenue Maximization Algorithm with Endogenous Sampling

Author

Listed:
  • Xiaotie Deng
  • Ron Lavi
  • Tao Lin
  • Qi Qi
  • Wenwei Wang
  • Xiang Yan

Abstract

The Empirical Revenue Maximization (ERM) is one of the most important price learning algorithms in auction design: as the literature shows it can learn approximately optimal reserve prices for revenue-maximizing auctioneers in both repeated auctions and uniform-price auctions. However, in these applications the agents who provide inputs to ERM have incentives to manipulate the inputs to lower the outputted price. We generalize the definition of an incentive-awareness measure proposed by Lavi et al (2019), to quantify the reduction of ERM's outputted price due to a change of $m\ge 1$ out of $N$ input samples, and provide specific convergence rates of this measure to zero as $N$ goes to infinity for different types of input distributions. By adopting this measure, we construct an efficient, approximately incentive-compatible, and revenue-optimal learning algorithm using ERM in repeated auctions against non-myopic bidders, and show approximate group incentive-compatibility in uniform-price auctions.

Suggested Citation

  • Xiaotie Deng & Ron Lavi & Tao Lin & Qi Qi & Wenwei Wang & Xiang Yan, 2020. "A Game-Theoretic Analysis of the Empirical Revenue Maximization Algorithm with Endogenous Sampling," Papers 2010.05519, arXiv.org.
  • Handle: RePEc:arx:papers:2010.05519
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    References listed on IDEAS

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    1. Goldberg, Andrew V. & Hartline, Jason D. & Karlin, Anna R. & Saks, Michael & Wright, Andrew, 2006. "Competitive auctions," Games and Economic Behavior, Elsevier, vol. 55(2), pages 242-269, May.
    2. Devanur, Nikhil R. & Peres, Yuval & Sivan, Balasubramanian, 2019. "Perfect Bayesian Equilibria in repeated sales," Games and Economic Behavior, Elsevier, vol. 118(C), pages 570-588.
    3. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
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    Cited by:

    1. Xiaotie Deng & Xinyan Hu & Tao Lin & Weiqiang Zheng, 2021. "Nash Convergence of Mean-Based Learning Algorithms in First Price Auctions," Papers 2110.03906, arXiv.org, revised Feb 2023.

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