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Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework

Author

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  • Emmanuel Guerre
  • Yao Luo

Abstract

We consider nonparametric identification of independent private value first-price auction models, in which the analyst only observes winning bids. Our benchmark model assumes an exogenous number of bidders N. We show that, if the bidders observe N, the resulting discontinuities in the winning bid density can be used to identify the distribution of N. The private value distribution can be nonparametrically identified in a second step. This extends, under testable identification conditions, to the case where N is a number of potential buyers, who bid with some unknown probability. Identification also holds in presence of additive unobserved heterogeneity drawn from some parametric distributions.

Suggested Citation

  • Emmanuel Guerre & Yao Luo, 2026. "Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework," Working Papers tecipa-827, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-827
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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