Nota di Lavoro, Fondazione Eni Enrico Mattei 153.2004
The seller of N distinct objects is uncertain about the buyers valuation for those objects. The sellers problem, to maximize expected revenue, consists of maximizing a linear functional over a convex set of mechanisms. A solution to the sellers problem can always be found in an extreme point of the feasible set. We identify the relevant extreme points and faces of the feasible set. With N = 1, the extreme points are easily described providing simple proofs of well-known results. The revenue-maximizing mechanism assigns the object with probability one or zero depending on the buyers report. With N > 1, extreme points often involve randomization in the assignment of goods. Virtually any extreme point of the feasible set maximizes revenue for a well-behaved distribution of buyers valuations. We provide a simple algebraic procedure to determine whether a mechanism is an extreme point.
Extreme point Exposed point Faces Non-linear pricing Monopoly pricing Multidimensional Screening Incentive compatibility Adverse selection Mechanism design