When Can Auctions Maximize Post-Auction Welfare?

I study auctions in which firms bid for licenses that reduce their marginal costs in a post-auction downstream market. When there are three or more firms, I show that the Vickrey--Clarke--Groves (VCG) auction maximizes consumer surplus in dominant strategies if and only if it maximizes producer surplus in dominant strategies. With two firms, the effect on consumer surplus is ambiguous. When the VCG auction does not maximize consumer surplus, I show that consumer surplus can be maximized by adding the right caps, i.e., restricting the number of licenses a bidder can win. This might lower producer surplus.