Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly
AbstractThe 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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Bibliographic InfoPaper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.153.
Date of creation: Dec 2004
Date of revision:
Extreme point; Exposed point; Faces; Non-linear pricing; Monopoly pricing; Multidimensional; Screening; Incentive compatibility; Adverse selection; Mechanism design;
Other versions of this item:
- Manelli, Alejandro M. & Vincent, Daniel R., 2007. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly," Journal of Economic Theory, Elsevier, vol. 137(1), pages 153-185, November.
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-01-16 (All new papers)
- NEP-GTH-2005-01-16 (Game Theory)
- NEP-MIC-2005-01-16 (Microeconomics)
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