Auctions with Signaling Concerns

We study a symmetric private value auction with signaling, in which the auction outcome is used by an outside observer to infer the bidders' types. We elicit conditions under which an essentially unique D1 equilibrium bidding function exists in four auction formats: first-price, second-price, all-pay and the English auction. We obtain a strict ranking in terms of expected revenues: the first-price and all-pay auctions dominate the English auction but are dominated by the second-price auction.