Stochastic vs Deterministic Mechanisms in Multidimensional Screening

Abstract

This paper studies the multidimensional screening problem of a profit-maximizing monopolist who designs and sells goods with multiple indivisible attributes. The buyer’s utility is linear in the probabilities of obtaining the attributes. The values of the attributes are buyer’s private information. The paper solves the seller’s problem for an arbitrary number of attributes when there are two types of buyers. When there is a continuum of buyer types, the paper shows that generically the seller wants to sell goods with some of the attributes partly damaged, stochastic, or leased on restrictive terms. In particular, the often-studied simple bundling strategies are shown to be generically suboptimal. This last result is qualified in the case of two buyer types. In this case, the maximum seller’s loss from the restriction to simple bundling is 12.5%.