  We study a seller who sells a single good to multiple bidders with
uncertainty over the joint distribution of bidders' valuations, as well as
bidders' higher-order beliefs about their opponents. The seller only knows the
(possibly asymmetric) means of the marginal distributions of each bidder's
valuation and the range. An adversarial nature chooses the worst-case
distribution within this ambiguity set along with the worst-case information
structure. We find that a second-price auction with a symmetric, random reserve
price obtains the optimal revenue guarantee within a broad class of mechanisms
we refer to as competitive mechanisms, which include standard auction formats,
including the first-price auction, with or without reserve prices. The optimal
mechanism possesses two notable characteristics. First, the mechanism treats
all bidders identically even in the presence of ex-ante asymmetries. Second,
when bidders are identical and the number of bidders $n$ grows large, the
seller's optimal reserve price converges in probability to a non-binding
reserve price and the revenue guarantee converges to the best possible revenue
guarantee at rate $O(1/n)$.
