Robustly Optimal Reserve Price

Abstract

We study a robust version of the single-unit auction problem. The auctioneer has confidence in her estimate of the marginal distribution of a generic bidder's valuation, but does not have reliable information about the joint distribution. In this setting, we analyze the performance of second-price auctions with reserve prices in terms of revenue guarantee, that is, the greatest lower bound of revenue across all joint distributions that are consistent with the marginals. For any finite number of bidders, we solve for the robustly optimal reserve price that generates the highest revenue guarantee. Our analysis has interesting implications in large markets. For any marginal distribution, the robustly optimal reserve price converges to zero as the number of bidders gets large. Furthermore, the second-price auction with no reserve price is asymptotically optimal among all mechanisms.