Interim Information and Seller’s Revenue in Standard Auctions

We study the interim seller’s revenue — the expected revenue conditional on the valuation of one bidder — in a class of sealed-bid auctions that are ex-ante equivalent by the Revenue Equivalence Theorem. Interim revenue differences across auction formats depend on the expected transfer of a generic bidder conditional on a competitor’s valuation. The first-price auction yields higher (lower) interim revenue than the second-price auction if the valuation is below (above) a threshold. At the lowest possible valuation, the first-price auction also yields the highest interim revenue among all standard auctions. By contrast, at high valuations the first-price auction yields the lowest interim revenue, while the last-pay auction — an atypical mechanism where only the lowest bidder pays — allows the seller to extract arbitrarily large revenues.