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Multiple Equilibria in Asymmetric First-Price Auctions

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  • Todd R. Kaplan
  • Shmuel Zamir

Abstract

Maskin and Riley (2003) and Lebrun (2006) prove that the Bayes-Nash equilibrium of first-price auctions is unique. This uniqueness requires the assumption that a buyer never bids above his value. We demonstrate that, in asymmetric first-price auctions (with or without a minimum bid), the relaxation of this assumption results in additional equilibria that are "substantial." Although in each of these additional equilibria no buyer wins with a bids above his value, the allocation of the object and the selling price may vary among the equilibria. Furthermore, we show that such phenomena can only occur under asymmetry in the distributions of values.

Suggested Citation

  • Todd R. Kaplan & Shmuel Zamir, 2011. "Multiple Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp591, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp591
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    References listed on IDEAS

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    1. Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November.
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    3. Blume, Andreas & Heidhues, Paul & Lafky, Jonathan & Münster, Johannes & Zhang, Meixia, 2006. "All Nash Equilibria of the Multi-Unit Vickrey Auction," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 116, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
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    9. 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.
    10. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    11. Maschler,Michael & Solan,Eilon & Zamir,Shmuel, 2013. "Game Theory," Cambridge Books, Cambridge University Press, number 9781107005488.
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    Cited by:

    1. Cole, Matthew T. & Davies, Ronald B. & Kaplan, Todd, 2017. "Protection in government procurement auctions," Journal of International Economics, Elsevier, vol. 106(C), pages 134-142.
    2. Kirkegaard, René, 2014. "Ranking asymmetric auctions: Filling the gap between a distributional shift and stretch," Games and Economic Behavior, Elsevier, vol. 85(C), pages 60-69.
    3. Martin Bichler & Nils Kohring & Stefan Heidekrüger, 2023. "Learning Equilibria in Asymmetric Auction Games," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 523-542, May.
    4. Domenico Colucci & Nicola Doni & Vincenzo Valori, 2015. "Information policies in procurement auctions with heterogeneous suppliers," Journal of Economics, Springer, vol. 114(3), pages 211-238, April.

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    More about this item

    Keywords

    asymmetric auctions; first-price auctions; multiple equilibria;
    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

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