First price auctions: Monotonicity and uniqueness

Gustavo Rodríguez

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

Abstract: I study monotonicity and uniqueness of the equilibrium strategies in a two-person first price auction with affiliated signals. I show that when the game is symmetric there is a unique Nash equilibrium that satisfies a regularity condition requiring that the equilibrium strategies be {\sl piecewise monotone}. Moreover, when the signals are discrete-valued, the equilibrium is unique. The central part of the proof consists of showing that at any regular equilibrium the bidders' strategies must be monotone increasing within the support of winning bids. The monotonicity result derived in this paper provides the missing link for the analysis of uniqueness in two-person first price auctions. Importantly, this result extends to asymmetric auctions.

Keywords: Auctions; game theory (search for similar items in EconPapers)
JEL-codes: C72 D44 (search for similar items in EconPapers)
Date: 1997-02
New Economics Papers: this item is included in nep-gth and nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:208

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