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On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions

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  • Philip J. Reny

    ()

  • Shmuel Zamir

    ()

Abstract

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.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp292.

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Length: 28 pages
Date of creation: Jun 2002
Date of revision:
Publication status: Published in Econometrica, 2004, vol. 72, pp. 1105-1125.
Handle: RePEc:huj:dispap:dp292

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Keywords: First-Price Auction; Monotone Equilibrium; Pure Strategy;

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  1. 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.
  2. 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.
  3. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
  4. Gustavo E. Rodriguez, 2000. "First price auctions: Monotonicity and uniqueness," International Journal of Game Theory, Springer, vol. 29(3), pages 413-432.
  5. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  6. 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.
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