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Revenue Guarantee Equivalence

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  • Bergemann, Dirk
  • Brooks, Benjamin A
  • Morris, Stephen

Abstract

We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders' values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions all have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks and Morris (2017). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered.

Suggested Citation

  • Bergemann, Dirk & Brooks, Benjamin A & Morris, Stephen, 2018. "Revenue Guarantee Equivalence," CEPR Discussion Papers 12964, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:12964
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    References listed on IDEAS

    as
    1. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Optimal Auction Design in a Common Value Model," Working Papers 085_2016, Princeton University, Department of Economics, Econometric Research Program..
    2. Jeremy Bulow & Paul Klemperer, 2002. "Prices and the Winner's Curse," RAND Journal of Economics, The RAND Corporation, vol. 33(1), pages 1-21, Spring.
    3. Hanming Fang & Stephen Morris, 2012. "Multidimensional Private Value Auctions," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 9, pages 319-356, World Scientific Publishing Co. Pte. Ltd..
    4. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Informationally Robust Optimal Auction Design," Cowles Foundation Discussion Papers 2065, Cowles Foundation for Research in Economics, Yale University.
    5. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January.
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    Cited by:

    1. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2024.
    2. Kim, Kyungmin & Koh, Youngwoo, 2022. "Auctions with flexible information acquisition," Games and Economic Behavior, Elsevier, vol. 133(C), pages 256-281.
    3. Abraham, Ittai & Athey, Susan & Babaioff, Moshe & Grubb, Michael D., 2020. "Peaches, lemons, and cookies: Designing auction markets with dispersed information," Games and Economic Behavior, Elsevier, vol. 124(C), pages 454-477.
    4. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    5. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    6. Pycia, Marek & Woodward, Kyle, 2021. "Auctions of Homogeneous Goods: A Case for Pay-as-Bid," CEPR Discussion Papers 15656, C.E.P.R. Discussion Papers.

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    More about this item

    Keywords

    Revenue guarantee; Common values; Affiliated values; Revenue equivalence; Revenue ranking; First-price auction; Second-price auction; English auction;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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