Auction design with opportunity cost

This paper studies revenue-maximizing auctions in an independent private value setting where potential bidders have known positive opportunity cost of bidding. The main findings are as follows. Firstly, there is no loss of generality in deriving the revenue-maximizing auctions within the class of threshold-entry mechanisms. Secondly, for any given set of entry thresholds, a second-price sealed-bid auction with properly set reserve prices and entry subsidy is revenue-maximizing. Thirdly, a variety of auctions are revenue-maximizing within the symmetric threshold-entry class. Two of them involve no entry subsidy (fee). Fourthly, we identify sufficient conditions under which it is in the seller’s interest to limit the number of potential bidders even if the revenue-maximizing symmetric threshold-entry auction is adopted. Lastly, the revenue-maximizing auction implements asymmetric entry across symmetric bidders in many cases. I am grateful to Jean-Jacques Laffont for his advice. I thank Isabelle Brocas, Juan Carrillo, Indranil Chakraborty, Jeff Ely, Jinwoo Kim, Vijay Krishna, Preston McAfee, Isabelle Perrigne, Eric Rasmusen, Guofu Tan, Quang Vuong, Joseph Wang for helpful comments and suggestions. Insightful comments and suggestions from the associate editor and two anonymous referees have greatly improved the paper. Earlier versions have been presented at the 2004 International Industrial Organization Conference, the 2005 Pan Pacific Game Theory Conference and the 2007 International Game Theory Conference. All errors are mine. Financial support from National University of Singapore (R-122-000-088-112) is gratefully acknowledged.