We explore the impact of private information in sealed-bid ﬁrst-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indiﬀerent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identiﬁcation of value distributions from data on winning bids and for the informationally robust comparison of alternative bidding mechanisms.
First-price auction, information structure, Bayes correlated equilibrium, private values, interdependent values, common values, revenue, surplus, welfare bounds, reserve price.
JEL Classification Codes: C72, D44, D82, D83