On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions
AbstractWe establish the existence of pure strategy equilibria in monotone bidding functions in first-price auctions with asymmetric bidders, interdependent values and affiliated one-dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second-price auctions.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp292.
Length: 28 pages
Date of creation: Jun 2002
Date of revision:
Publication status: Published in Econometrica, 2004, vol. 72, pp. 1105-1125.
First-Price Auction; Monotone Equilibrium; Pure Strategy;
Other versions of this item:
- Philip J. Reny & Shmuel Zamir, 2004. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Econometrica, Econometric Society, vol. 72(4), pages 1105-1125, 07.
- NEP-ALL-2003-05-15 (All new papers)
- NEP-GTH-2003-05-15 (Game Theory)
- NEP-IND-2003-05-15 (Industrial Organization)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Athey, S., 1997.
"Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information,"
97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
- Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
- Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
- Gustavo E. Rodriguez, 2000. "First price auctions: Monotonicity and uniqueness," International Journal of Game Theory, Springer, vol. 29(3), pages 413-432.
- Milgrom, Paul R & Weber, Robert J, 1982.
"A Theory of Auctions and Competitive Bidding,"
Econometric Society, vol. 50(5), pages 1089-1122, September.
- 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.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ilan Nehama).
If references are entirely missing, you can add them using this form.