This paper considers auctions in which bidders compete for an advantage in future strategic interactions. Examples include bidding for patented innovations that reduce production costs, takeover battles, and the auctioning of licenses to operate in new markets (e.g. the recent spectrum auctions). We show that when bidders have an incentive to exaggerate their private information, equilibrium bids are biased upwards as bidders try to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids can be "above value," and may diverge to infinity for a strategic improvement everyone agrees is negligible. In English and first-price auctions, signaling is necessarily less extreme as the winning bidder incurs the cost of her signaling choice. Hence there is no strategic equivalence between the second-price and English auction in this independent private-information context (although revenue equivalence holds). In the English auction, the winner increases the winning bid after everyone else has dropped out. The opportunity to signal via the winning bid lowers bidders' expected payoffs and raises the seller's expected revenue, giving sellers an incentive to conceal information they may have about bidders' private valuations. Losers' profits are unaffected by the winner's attempt to signal since, in a separating equilibrium, losers can correctly infer the winner's information from the winning bid. We show that if bidders neglect the information contained in losing, i.e. a loser's curse, they may bid too high and end up winning a position they value much less ex post, a winner's curse. Finally, when bidders wish to understate their private information, a separating equilibrium need not exist. When it exists, however, signaling causes equilibrium bids to be biased downward in first-price and second-price auctions, while signaling is impossible in the English auction, which therefore yields higher revenues in this case.
