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.
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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, 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)
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- Eric Maskin & John Riley, 2003.
"Uniqueness of Equilibrium in Sealed High-Bid Auctions,"
Economics Working Papers
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- 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.
- Athey, Susan, 2001.
"Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information,"
Econometrica, Econometric Society,
Econometric Society, vol. 69(4), pages 861-89, July.
- Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
- Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 67(3), pages 439-54, July.
- 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.
- Paul Milgrom & Robert J. Weber, 1981.
"A Theory of Auctions and Competitive Bidding,"
Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science
447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Gustavo E. Rodriguez, 2000. "First price auctions: Monotonicity and uniqueness," International Journal of Game Theory, Springer, Springer, vol. 29(3), pages 413-432.
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