Optimal Discrimination-Free Auctions

This paper introduces a second-price auction with a flexible reserve price, where the reserve price for the top bidder is not fixed but rather determined as a function of all losing bids. We show that when bidders are ex ante heterogeneous, a second-price auction with an optimally chosen flexible reserve price not only generates strictly higher expected revenue than that of a second-price auction with any fixed reserve price but is also revenue-maximizing among all mechanisms that implement discrimination-free social choice functions. We also provide an axiomatic characterization of all second-price auctions with a flexible reserve price. Finally, we discuss real-life implementation. This paper was accepted by Martin Bichler, behavioral economics and decision analysis. Funding: This work was supported by Oesterreichische Nationalbank [Grant 19021] and the National Natural Science Foundation of China [Grant 72203148]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2024.04584 .