Auctions with Numerous Bidders

We study auctions in which the number of potential bidders is large, such as in Internet auctions. With numerous bidders, the expected revenue and the optimal bid function in a first price auction result in complicated expressions, except for a few simple distribution function for the bidders' valuations. We show that these expressions can be well approximated using extreme value theory without assuming a particular distribution function. The theory is applied to data from Internet auctions.