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 uncertain whether they will win or lose and indi˙erent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values.
We report further analytic and computational characterizations of revenue and bid-der surplus including upper bounds on revenue. Our work has implications for the identiﬁcation of value distributions from winning bid data and for the informationally robust comparison of alternative bidding mechanisms.