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

Alejandro Manelli and Daniel Vincent

No 2004.153, Working Papers from Fondazione Eni Enrico Mattei

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 (search for similar items in EconPapers)
JEL-codes: D44 (search for similar items in EconPapers)
Date: 2004-12
New Economics Papers: this item is included in nep-gth and nep-mic
References: Add references at CitEc
Citations: View citations in EconPapers (8)

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Related works:
Journal Article: Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly (2007)
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