Nonparametric estimation of utility function in first-price sealed-bid auctions

I propose a simple method to nonparametrically estimate the utility function in first-price, sealed-bid auctions when bidders’ participation is exogenous. Using a pair of bid densities, each for a different number of bidders, I establish a contraction mapping that converges to the true utility function. The method employs nonparametric estimates in place of the true bid densities to construct the contraction mapping and computes the utility function by iterating the contraction operator. A Monte Carlo study shows that the method approximates the true utility function and valuation density.