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First price auctions: Monotonicity and uniqueness

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  • Gustavo Rodríguez

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.

Suggested Citation

  • Gustavo Rodríguez, 1997. "First price auctions: Monotonicity and uniqueness," Economics Working Papers 208, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:208
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    References listed on IDEAS

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    1. Hendricks, Kenneth & Porter, Robert H & Wilson, Charles A, 1994. "Auctions for Oil and Gas Leases with an Informed Bidder and a Random Reservation Price," Econometrica, Econometric Society, vol. 62(6), pages 1415-1444, November.
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    More about this item

    Keywords

    Auctions; game theory;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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