We consider auctions with N “weak-valued” bidders and an \(N+1\) -th bidder who is “strong.” The auction is a “tournament” in which the weaker players bid to win the right to compete with the strong bidder. The sealed bids of all players are binding and the winning bid of the weaker players is entered in a second-price contest with the bid of the strong player. As we already noted in Anderlini and Kim (2024a), the tournament design of the auction generates “overbidding” by the weaker bidders. This is due to the fact that the only way for a weak bidder to win the auction is to win among the weak bidders. We let the values of the strong bidder converge in distribution to an atom above the upper end of the distribution of the weak bidders. If the rest of the distribution is drained away from low values sufficiently slowly, the auction’s expected revenue is arbitrarily close to the one obtained in a Myerson (1981) optimal auction. The auction design is “detail free” — no specific knowledge of the distributions is needed in addition to the identity of the stronger bidder. No information about the actual value of the limit large atom is required. This is important since mis-calibrating by a small amount an attempt to implement the optimal auction can lead to large losses in revenue.
