Multiple Equilibria in Asymmetric First-Price Auctions
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.
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- Eric Maskin & John Riley, 2003.
"Uniqueness of Equilibrium in Sealed High-Bid Auctions,"
Economics Working Papers
0031, Institute for Advanced Study, School of Social Science.
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- 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.
- Andreas Blume & Paul Heidhues & Jonathan Lafky & Johannes Muenster & Meixia Zhang, 2006. "All Nash Equilibria of the Multi-Unit Vickrey Auction," Working Papers 195, University of Pittsburgh, Department of Economics, revised Jan 2006.
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- Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer, vol. 50(2), pages 269-302, June.
- Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
- Blume, Andreas & Heidhues, Paul & Lafky, Jonathan & Münster, Johannes & Zhang, Meixia, 2009. "All equilibria of the multi-unit Vickrey auction," Games and Economic Behavior, Elsevier, vol. 66(2), pages 729-741, July.
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