Abstract
We consider an agent who has multiple dimensions of private information, and preferences that are additively separable across the various dimensions. (A canonical example is selling multiple goods to an agent with unknown values.) The standard revenue-maximization problem in this setting is difficult. Instead we consider a robust version of the problem: the principal knows the marginal distribution of each dimension of the agent's type, but does not know the joint distribution. Any mechanism is evaluated by its worst-case expected profit, over all joint distributions consistent with the known marginals. We show that the optimal mechanism is simply to separate across the dimensions, and use the optimum within each dimension. This requires no assumptions on the structure of preferences within each dimension.