FEEM working papers "Note di lavoro" series
2004 .153

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


Authors: Alejandro M. Manelli, Daniel R. Vincent
Series: Economy and Society
Editor: Fausto Panunzi
Type: Journal
Keywords: Extreme point,Exposed point,Faces,Non-linear pricing,Monopoly pricing,Multidimensional,Screening,Incentive compatibility,Adverse selection,Mechanism design
JEL n.: D44
JEL: Journal of Economic Theory
Pages: Vol. 137, Issue 1, pp.153-185
Date: 11/2007

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.

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