Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly

48 Pages Posted: 14 Jan 2005

See all articles by Alejandro Manelli

Alejandro Manelli

Arizona State University (ASU) - Economics Department

Daniel R. Vincent

University of Maryland - Department of Economics

Date Written: December 2004

Abstract

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.

Keywords: Extreme point, Exposed point, Faces, Non-linear pricing, Monopoly pricing, Multidimensional, Screening, Incentive compatibility, Adverse selection, Mechanism design

JEL Classification: D44

Suggested Citation

Manelli, Alejandro and Vincent, Daniel R., Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly (December 2004). Available at SSRN: https://ssrn.com/abstract=643586 or http://dx.doi.org/10.2139/ssrn.643586

Alejandro Manelli (Contact Author)

Arizona State University (ASU) - Economics Department ( email )

PO Box 873806
Tempe, AZ 85287-3806
United States
(480) 965-3531 (Phone)
(480) 965-0748 (Fax)

Daniel R. Vincent

University of Maryland - Department of Economics ( email )

College Park, MD 20742
United States
301-405-3485 (Phone)
301-405-3542 (Fax)

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