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Maximal Revenue with Multiple Goods: Nonmonotonicity and Other Observations

  • Sergiu Hart
  • Philip J. Reny

Consider the problem of maximizing the revenue from selling a number of goods to a single buyer. We show that, unlike the case of one good, when the buyer's values for the goods increase the seller's maximal revenue may well decrease. We also provide a characterization of revenue-maximizing mechanisms (more generally, of "seller-favorable" mechanisms) that circumvents nondifferentiability issues. Finally, through simple and transparent examples, we clarify the need for and the use of randomization when maximizing revenue in the multiple-goods versus the one-good case.

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Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp630.

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Length: 24 pages
Date of creation: Nov 2012
Date of revision:
Handle: RePEc:huj:dispap:dp630
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  1. Pavlov Gregory, 2011. "Optimal Mechanism for Selling Two Goods," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-35, February.
  2. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
  3. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-19, July.
  4. Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
  5. Sergiu Hart & Noam Nisan, 2014. "How Good Are Simple Mechanisms for Selling Multiple Goods?," Discussion Paper Series dp666, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  6. 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.
  7. Sergiu Hart & Noam Nisan, 2012. "Approximate Revenue Maximization with Multiple Items," Discussion Paper Series dp606, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  8. Motty Perry & Philip J. Reny, 1999. "On The Failure of the Linkage Principle in Multi-Unit Auctions," Econometrica, Econometric Society, vol. 67(4), pages 895-900, July.
  9. Menicucci Domenico, 2009. "Competition May Reduce the Revenue in a First Price Auction with Affiliated Private Values," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-19, December.
  10. Manelli, Alejandro M. & Vincent, Daniel R., 2006. "Bundling as an optimal selling mechanism for a multiple-good monopolist," Journal of Economic Theory, Elsevier, vol. 127(1), pages 1-35, March.
  11. Manelli, Alejandro M. & Vincent, Daniel R., 2012. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly. A corrigendum," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2492-2493.
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