Abstract:

We consider auctions with N + 1 bidders. Of these, N are symmetric
 and N+1 is su ciently strong relative to the others. The auction is a tournament
 in which the rst N players bid to win the right to compete with N + 1. The bids
 of the rst N players are binding and the highest bidder proceeds to a second-price
 competition with N +1.
 When N +1s values converge in distribution to an atom above the upper end of
 the distribution of the N bidders and the rest of the distribution is drained away from
 low values su ciently slowly, the auctions expected revenue is arbitrarily close to the
 one obtained in a Myerson (1981) optimal auction.
 The tournament design is detail free in the sense that no speci c knowledge of
 the distributions is needed in addition to the fact that bidder N + 1 is stronger than
 the others as required. In particular, no additional information about the value of the
 atom is needed. This is important since mis-calibrating by a small amount an attempt
 to implement the optimal auction can lead to large losses in revenue.
 We provide an interpretation of these results as possibly providing guidelines to a
 seller on how to strategically populate auctions with a single bidder even when only
 weaker bidders are available.