Distributionally Robust Pricing in Auctions

Abstract

Suppose that in a second-price auction, a seller wishes to set an optimal reserve price, but the information about the distribution of bidders’ iid valuations is scarce: the seller knows only an upper bound for valuations, the distribution’s mean, and, possibly, variance. I find reserve prices optimal in the sense of worst-case expected revenue maximization, where worst case is with respect to the unknown distribution. The optimal reserve price may not be unique, but the set of optimal prices always includes zero in the case when only mean is known.

Keywords: Auctions, Mechanism Design, Robustness, Distribution, Moment Constraints

JEL Classification: D44, D47, D80, D81, D82