EQUILIBRIUM BID FUNCTIONS FOR AUCTIONS WITH AN UNCERTAIN NUMBER OF BIDDERS

The number of rivals may be unknown when a bidding strategy is formulated in an auction. In a symmetric model with risk-neutral bidders holding independent information, we obtain explicit equilibrium bidding functions for first-price and second-price auctions with uncertainty about the number of rivals. Five auctions are revenue-equivalent: first-price and second-price auctions, each with the number of bidders known or uncertain, and English auctions. © 1990.