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Abstract:
Under the independent private value paradigm and symmetric best response bidding in a first-price auction, increasing the number of active bidders generates a bid distribution with an increasing support and a strictly positive density at the upper support bound. When buyers observe their number of competitors, the winning bid distribution has discontinuities that identifies this number. It turns out that the private value distribution is identified from the winning bid without assuming that the analyst observes the number of active bidders. Discontinuities of the winning bid probability density distribution also identifies the distribution of the number of active buyers. When buyers do not observe the number of competitors, the lack of discontinuities does not permit identification of the private value and number of bidders distributions. The auction outcome distribution is sufficient to identify auction models with random participation due to a reserve price or entry cost when buyers observe the number of competitors, and when they do not under an additional exclusion restriction. The auction outcome also identify whether buyers observe or not the number of their competitors or whether participation is driven by a reserve price or entry cost.
