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

Author

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  • Alejandro M. Manelli

    (W.P. Carey School of Business, Arizona State University)

  • Daniel R. Vincent

    (University of Maryland)

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.

Suggested Citation

  • Alejandro M. Manelli & Daniel R. Vincent, 2004. "Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly," Working Papers 2004.153, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2004.153
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    References listed on IDEAS

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    More about this item

    Keywords

    Extreme point; Exposed point; Faces; Non-linear pricing; Monopoly pricing; Multidimensional; Screening; Incentive compatibility; Adverse selection; Mechanism design;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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