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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. Copyright The Econometric Society 2004.

Suggested Citation

  • 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, July.
    • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:4:p:1105-1125
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00527.x
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