Consider a government tendering a facility, such as an airport or railway, when one of the bidders is an 'existing operator' who owns another facility that is a substitute or complement to the tendered facility. In 'standard auctions', bidders compete on how much to pay to the government. We find that, all else equal, the existing operator offers to pay more than a 'new bidder' and the operator is therefore more likely to win the auction. In consumer-price auctions, bidders compete on the price they will charge. New bidders offer to set the price at their marginal cost. With complements, the existing operator strategically offers a price that is below its marginal cost; with substitutes, it offers a price that is above its marginal cost. Price auctions are better for welfare than standard auctions: they lead to lower mark-ups and are less affected by having an existing operator in the auction.