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

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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.

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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.153.

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Date of creation: Dec 2004
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Handle: RePEc:fem:femwpa:2004.153

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

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  1. McAfee, R Preston & McMillan, John & Whinston, Michael D, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, MIT Press, vol. 104(2), pages 371-83, May.
  2. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
  3. Basov, Suren, 2001. "Hamiltonian approach to multi-dimensional screening," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 77-94, September.
  4. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
  5. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
  6. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  7. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1999. "Multidimensional Mechanism Design for Auctions with Externalities," Journal of Economic Theory, Elsevier, vol. 85(2), pages 258-293, April.
  8. Adams, William James & Yellen, Janet L, 1976. "Commodity Bundling and the Burden of Monopoly," The Quarterly Journal of Economics, MIT Press, vol. 90(3), pages 475-98, August.
  9. Riley, John & Zeckhauser, Richard, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, MIT Press, vol. 98(2), pages 267-89, May.
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Cited by:
  1. Sergiu Hart & Philip J. Reny, 2012. "Maximal Revenue with Multiple Goods: Nonmonotonicity and Other Observations," Discussion Paper Series dp630, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. John Asker & Estelle Cantillon, 2010. "Procurement when price and quality matter," RAND Journal of Economics, RAND Corporation, vol. 41(1), pages 1-34.
  3. Sergiu Hart & Noam Nisan, 2012. "Approximate Revenue Maximization with Multiple Items," Discussion Paper Series dp606, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. Sandro Brusco & Giuseppe Lopomo & Leslie M. Marx, 2008. "The Economics of Contingent Re-Auctions," Department of Economics Working Papers 08-02, Stony Brook University, Department of Economics.
  5. Mehmet Ekmekci & Nenad Kos & Rakesh Vohra, 2013. "Just Enough or All: Selling a Firm," Working Papers 470, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  6. Omer Lev, 2010. "A Two-Dimensional Problem of Revenue Maximization," Discussion Paper Series dp542, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  7. Asker, John & Cantillon, Estelle, 2005. "Optimal Procurement When Both Price and Quality Matter," CEPR Discussion Papers 5276, C.E.P.R. Discussion Papers.
  8. Alexey Malakhov & Rakesh Vohra, 2009. "An optimal auction for capacity constrained bidders: a network perspective," Economic Theory, Springer, vol. 39(1), pages 113-128, April.
  9. Lev, Omer, 2011. "A two-dimensional problem of revenue maximization," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 718-727.

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