Distributionally robust pricing in independent private value auctions

Abstract

A seller chooses a reserve price in a second-price auction to maximize worst-case expected revenue when she knows only the mean of value distribution and an upper bound on either values themselves or variance. Values are private and iid. Using an indirect technique, we prove that it is always optimal to set the reserve price to the seller's own valuation. However, the maxmin reserve price may not be unique. Sometimes it is optimal to choose a deterministic reserve price even when randomization is allowed, which is unusual for maxmin settings. A second-price auction with the reserve equal to seller's value is an asymptotically optimal mechanism (among all ex post individually rational mechanisms) as the number of bidders grows without bound.