A principal allocates a single good to one of several agents whose values are privately and independently distributed, employing an optimal mechanism. The principal shapes the distribution of the agents' values within general classes of constraints. Divisive product designs, which are either...

In many competitive settings consumers buy multiple product categories, and some prefer to use a single firm, generating complementary cross-category price effects. To study pricing in supermarkets, an organizational form where these effects are internalized, we develop a multi-category...