When bidders have correlated private information, optimal auction mechanisms screen bidders based on their beliefs. We show that the possibility of ex post withdrawal by bidders provides a foundation for uniform price auctions that applies even in settings with correlated information. Withdrawal rights therefore provide a realistic framework for studying optimal auction design with correlated information. Our results are not driven by ex post individual rationality constraints or their interaction with the winner's curse. Instead, our analysis relies on a strategic impact of withdrawal rights: bidders can engage in "double deviations" that involve misreporting and then (sometimes) withdrawing ex post.

A monopolist wants to sell multiple goods, accounting for the possibility of returns. For any bundle purchased, a buyer can return any part of the bundle for a partial refund specified by a return policy. The seller is constrained to offer additive return policies: the total price of a bundle must be divided into return values for each of the goods in the bundle. We show that if the buyer's values are additive and independent across goods, then selling each good separately is optimal. The result applies even if the seller can use stochastic mechanisms, and holds for general multidimensional screening problems. We show that selling separately remains approximately optimal if the buyer experiences small return costs, as well as if the return policy only has to be close to additive or the buyer's values are weakly correlated. Applying our analysis to multiproduct pricing without returns, we introduce a new concept of bundle discounts and show that obtaining revenue gains from using any complex mechanism requires discounting bundles in our sense.