Revenue guarantee equivalence

We revisit the revenue comparison of standard auction formats, including frst-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fxed the distribution of bidders' values. We conclude that if we restrict attention to the symmetric affliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, frst-price, second-price, and English auctions are revenue guarantee equivalent: they have the same revenue guarantee, which is equal to that of the frst-price auction as characterized by Bergemann, Brooks, and Morris (2017). If we consider all equilibria or if we allow more general models of information, then frst-price auctions have a greater revenue guarantee than all other auctions considered.