On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions
We 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.
|Date of creation:||Jun 2002|
|Date of revision:|
|Publication status:||Published in Econometrica, 2004, vol. 72, pp. 1105-1125.|
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- Gustavo E. Rodriguez, 2000. "First price auctions: Monotonicity and uniqueness," International Journal of Game Theory, Springer, vol. 29(3), pages 413-432.
- 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.
- 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.
- Milgrom, Paul R & Weber, Robert J, 1982.
"A Theory of Auctions and Competitive Bidding,"
Econometric Society, vol. 50(5), pages 1089-1122, September.
- 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.
- 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.
- Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
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