Ironing, Sweeping, and Multivariate Majorization

The authors study the sale of an excludable, non-rival good by a monopolist when buyers’ values are interdependent, i.e. buyers’ utilities from consuming the good depend on their own and others’ information. Most mass-produced goods fit this framework. They develop a constructive approach to deal with incentive compatibility constraints and thereby characterize the profit-maximizing mechanism. In particular, the paper exploits the structure of the Kuhn-Tucker conditions resulting from the constrained optimizationproblem to define a novel multivariate majorization concept. The majorization technique allows them to generalize Mussa and Rosen’s (1978) “ironing” to settings with multidimensional information. The authors also relate the majorization approach to Rochet and Choné’s (1998) “sweeping” method. They illustrate how discriminatory access rights lead to constrained majorization, resulting in higher seller profits as well as a more efficient production of mass-produced goods.