Does a Seller Really Want Another Bidder?

Jeremy I. Bulow and Paul D. Klemperer (AER, 1996) argue that the usual concerns of auction design miss the big picture, and show that a simple English auction without a reserve price and N + 1 bidders attains expected revenue in excess of any auction with N bidders. The issue of how this additional bidder might be attracted is not treated in their model. In fact, that an auction can convince another bidder it is worth his while to compete carries a critical message about expected revenue. In those many markets where potential bidders decide whether to compete in an auction based on the expected probability of bidding, Bulow and Klemperer's conclusion is shown here to be overturned. I explore the symmetric equilibrium of a model where potential bidders first decide whether to participate in an auction, and then participants select bidding strategies. Expected revenue is increased by some degree of bidder discouragement, in that it is never optimal to have all N potential bidders participate with probability one, even for very small N