Identification and Optimal Reserve Prices in Ascending Auctions, with an Application to Art

Abstract: This paper proposes a novel non-parametric approach to partial identification of the distribution of the highest valuation, seller’s expected profit, and optimal reserve price in symmetric ascending auctions. Our approach restricts the distribution of valuations away from the pure common- and independent private values settings, leading to substantially tighter bounds. It also accommodates an unknown number of bidders, as long as bounds on it are available. Additionally, we formulate and solve the Min-Max-Regret problem of the seller choosing a reserve price while facing ambiguity about the distribution of valuations. We apply the proposed methodology to a new dataset consisting of more than 3500 art auctions held by the two largest auction houses, Christie’s and Sotheby’s. For Modern Art sold in New York City priced between $1.0M and $10.0M, we find that setting reserve prices 26% higher would increase the seller’s expected profit by at least $126K per lot, or $3.8M per auction.