Robustness and Separation in Multidimensional Screening

A principal wishes to screen an agent along several dimensions simultaneously. The agent has quasilinear preferences that are additively separable across the various components. We consider a robust version of the principal’s problem, in which she knows the marginal distribution of each component 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 optimum for the principal is simply to screen along each component separately. This result does not require any assumptions (such as single-crossing) on the structure of preferences within each component. Applications of the model include monopoly pricing and dynamic taxation. This paper has greatly benefited from conversations with Florian Scheuer, as well as helpful comments from (in random order) Richard Holden, Dawen Meng, Andy