The seller of N distinct objects is uncertain about the buyer's valuation for those objects. The seller's problem, to maximize expected revenue, consists of maximizing a linear functional over a convex set of mechanisms. A solution to the seller's problem can always be found in an extreme point of the feasible set.
Multi-Dimensional Mechanism Design: Revenue Maximization and the Multiple Good MonopolyAlejandro Manelli and Daniel R. Vincent ,
1( 137 )
Journal of Economic Theory