Ironing, Sweeping, and Multidimensional Screening

The authors provide existence proofs and characterization results for the multidimensional version of the multiproduct monopolist problem of M. Mussa and S, Rosen (1978). These results a are also directly applicable to the multidimensional nonlinear pricing problems studied by R. Wilson (1993) and M. Armstrong (1996). The authors establish that bunching is robust in these multidimensional screening problems, even with very regular distributions of types. They consequently design a new technique, the sweeping procedure, for dealing with bunching in multidimensional contexts. This technique extends the ironing procedure of Mussa and Rosen to several dimensions.