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

Philip Reny () and Shmuel Zamir ()

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

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.

Keywords: First-Price Auction; Monotone Equilibrium; Pure Strategy (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth and nep-ind
Date: 2002-06
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Published in Econometrica, 2004, vol. 72, pp. 1105-1125.

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