Multiple equilibria in asymmetric first-price auctions

Kaplan, Todd R and Zamir, Shmuel (2011): Multiple equilibria in asymmetric first-price auctions.

Abstract

Maskin and Riley (2003) and Lebrun (2006) prove that the Bayes-Nash equilibrium of �rst-price auctions is unique. This uniqueness requires the assumption that a buyer never bids above his value. We demonstrate that, in asymmetric �rst-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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Asymmetric auctions, �first-price auctions, multiple equilibria
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D44 - Auctions; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Baye, M., and J. Morgan (1999): "A folk theorem for one-shot Bertrand games,"Economics Letters, 65(1), 59-65.

Binmore, K. (1999): "Why experiment in economics?," The Economic Journal, 109(453), 16-24.

Blume, A., and P. Heidhues (2004): "All equilibria of the Vickrey auction," Journal of Economic Theory, 114(1), 170-177.

Blume, A., P. Heidhues, J. Lafky, J. Münster, and M. Zhang (2009): "All equilibria of the multi-unit Vickrey auction," Games and Economic Behavior, 66(2), 729-741.

Erlei, M. (2002): "Some forgotten equilibria of the Bertrand duopoly!?," TUC Working Paper.

Kaplan, T., and D. Wettstein (2000): "The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition," Spanish Economic Review, 2(1), 65-71.

Kaplan, T., and S. Zamir (2011a): "Asymmetric �first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, forthcoming.

Kaplan, T., and S. Zamir (2011b): "Comparative Statics of a Minimum Bid in Asymmetric First-Price Auctions," Working Paper.

Lebrun, B. (2006): "Uniqueness of the equilibrium in �rst-price auctions," Games and Economic Behavior, 55(1), 131-151.

Maskin, E., and J. Riley (2003): "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, 45(2), 395-409.

McAdams, D. (2007): "Uniqueness in symmetric �first-price auctions with affiliation," Journal of Economic Theory, 136(1), 144-166.

Vickrey, W. (1961): "Counterspeculation, auctions, and competitive sealed tenders,"Journal of Finance, 16(1), 8-37.