Nonparametric Identification and Estimation of Double Auctions With Bargaining

This article studies the nonparametric identification and estimation of double auctions with one buyer and one seller. This model assumes that both bidders submit their own sealed bids, and the transaction price is determined by a weighted average between the submitted bids when the buyer’s offer is higher than the seller’s ask. It captures the bargaining process between two parties. Working within this double auction model, we first establish the nonparametric identification of both the buyer’s and the seller’s private value distributions in two bid data scenarios; from the case of all bids being available, to the case of only transacted bids being available. Specifically, both private value distributions are point identified when all of the bids are observed. They are, however, partially identified when only the transacted bids are available. In the latter case, a sharp characterization of the identified set is provided. Second, we estimate double auctions with bargaining using a two-step procedure that incorporates both boundary and interior bias correction. We then show that our value density estimators achieve the optimal uniform convergence rate of first-price auctions. Monte Carlo experiments show that, in finite samples, our estimation procedure works well on the whole support.

Common value auction · Database transaction · Estimator · Monte Carlo method · Nonparametric statistics · Auction Theory and Applications · Consumer Market Behavior and Pricing · Game Theory and Voting Systems

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