Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly
Arizona State University (ASU) - Economics Department
Daniel R. Vincent
University of Maryland - Department of Economics
FEEM Working Paper No. 153.04
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. 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 buyer's 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 buyer's valuations. We provide a simple algebraic procedure to determine whether a mechanism is an extreme point.
Number of Pages in PDF File: 48
Keywords: Extreme point, Exposed point, Faces, Non-linear pricing, Monopoly pricing, Multidimensional, Screening, Incentive compatibility, Adverse selection, Mechanism design
JEL Classification: D44working papers series
Date posted: January 14, 2005
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