Bundling and optimal auctions of multiple products

We study the optimal (i.e. revenue maximizing) auction of multiple products . We make three major points. First, we extend the relationship between pri ce discrimination and optimal auctions from the single-product case to the multiple-product case. A monopolist setting prices for multiple products ma y offer discounts on purchases of bundles of products; similarly, the optim al auction of multiple products facilitates price discrimination by allocat ing products inefficiently to customers who are willing to purchase both pr oducts. Second, we demonstrate that optimal auctions are qualitatively dist inct from monopoly sales of multiple products. Because of uncertainty about the values of other consumers, two products are bundled probabilistically in an optimal auction for a customer who is willing to buy both of them. A customer may then receive a discount on a lower-valued product without rece iving a higher-valued product. Third, we show that in an optimal auction of two products the allocation of one product may vary with the amount of com petition for the other product.