Auctions with heterogeneous entry costs

If bidders have independent private values and homogeneous entry costs, a first- or second-price auction with a reserve price equal to the seller's value maximizes social surplus and seller revenue. We show that if entry costs are heterogeneous and private information, then the revenue-maximizing reserve price is above the seller's value, a positive admission fee (and a reserve price equal to the seller's value) generates more revenue, and an entry cap combined with an admission fee generates even more revenue. Social surplus and seller revenue may either increase or decrease in the number of bidders, but they coincide asymptotically.