Bundling and Optimal Auctions of Multiple Products
研究多产品最优拍卖（收入最大化），将单产品最优拍卖与价格歧视的关系扩展到多产品情形，证明最优拍卖与垄断定价有本质区别，并揭示两产品拍卖中分配相互依赖。
We study the optimal (i.e. revenue maximizing) auction of multiple products. We make three major points. First, we extend the relationship between price discrimination and optimal auctions from the single-product case to the multiple-product case. A monopolist setting prices for multiple products may offer discounts on purchases of bundles of products; similarly, the optimal auction of multiple products facilitates price discrimination by allocating products inefficiently to customers who are willing to purchase both products. Second, we demonstrate that optimal auctions are qualitatively distinct 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 receiving 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 competition for the other product.