Optimal Second Price Auctions with Positively Correlated Private Values and Limited Information

Closely related to the work of Athey and Haile (2002), we consider the problem of maximizing revenue in a second-price private-values auction with only limited data from previous auctions. We find that, when bidder values for the object being sold are not assumed to be distributed independently, the optimal levels of the reserve price and (when available) entry fee are not uniquely identified, and can vary over a significant range. Further, under two common representations of positively correlated values, the optimal values of these parameters tend to be lower than analysis assuming independence would have suggested. While this is written as a theory paper, the well-publicized use of auctions by the government (spectrum auctions, procurement auctions, and others) means that any work on how to best run an auction, and on the data requirements and difficulties in running an auction optimally, has clear policy implications.