Asymmetric common-value auctions with applications to private-value auctions with resale

We study a model of common-value auctions with two bidders in which bidders’ private information are independently and asymmetrically distributed. We present sufficient and necessary conditions, respectively, under which the expected revenues from first-price and second-price auctions can be ranked. Using these conditions and a bid-equivalence between common-value auctions and private-value auctions with resale, we extend the revenue-ranking result of Hafalir and Krishna [Am Econ Rev 98, 2008a] and provide necessary conditions for their ranking to hold. In addition, we provide sufficient and necessary conditions for the opposite ranking of revenues, respectively. Our analysis helps clarify the roles of two forms of regularity assumptions (buyer-regularity and seller-regularity) in ranking revenues and illustrates how revenue ranking is linked to submodularity and supermodularity of the common-value function and to a single-crossing property of a function derived from the monopoly or monopsony pricing function in the resale stage.