Robust auctions with affiliated private values

We study auctions in an affiliated private value framework in which buyers face ambiguity over the distribution of the others' valuations and make choices that are robust to that ambiguity. We show that, in contrast to the Bayesian case, a first-price auction can generate a higher revenue than a second-price auction in the presence of ambiguity. We also extend this insight to large double auctions. In particular, we propose a pay-as-bid double auction mechanism and demonstrate that given any nontrivial amount of ambiguity, this mechanism implements the efficient trade and is ex-post budget balanced with probability one as the market size grows.