Private and common value auctions with ambiguity over correlation

Abstract

We analyze auctions when individuals have ambiguity over the joint information structures generating the valuations and signals of players. We analyze how two standard auction effects interact with the ambiguity of bidders over correlation structures. First, a “competition effect” arises when different beliefs about the correlation between bidders' valuations imply different likelihoods of facing competitive bids. Second, a “winner's value effect” arises when different beliefs imply different inferences about the winner's value. In the private values case, only the first effect exists and this implies that the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist and we show that compared to the canonical model, both in the first-price and second-price auctions, these effects combine to imply that the seller's revenue decreases with ambiguity (in contrast with the private values case). We then characterise the optimal auction in both the private and common value cases. A novel feature that arises in the optimal mechanism in the common values case is that the seller only partially insures the high type against ambiguity.