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Approximate Revenue Maximization with Multiple Items

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  • Sergiu Hart
  • Noam Nisan

Abstract

Myerson’s classic result provides a full description of how a seller can maximize revenue when selling a single item. We address the question of revenue maximization in the simplest possible multi-item setting: two items and a single buyer who has independently distributed values for the items, and an additive valuation. In general, the revenue achievable from selling two independent items may be strictly higher than the sum of the revenues obtainable by selling each of them separately. In fact, the structure of optimal (i.e., revenue-maximizing) mechanisms for two items even in this simple setting is not understood. In this paper we obtain approximate revenue optimization results using two simple auctions: that of selling the items separately, and that of selling them as a single bundle. Our main results (which are of a “direct sum” variety, and apply to any distributions) are as follows. Selling the items separately guarantees at least half the revenue of the optimal auction; for identically distributed items, this becomes at least 73% of the optimal revenue. For the case of k > 2 items, we show that selling separately guarantees at least a c/log^2 k fraction of the optimal revenue; for identically distributed items, the bundling auction yields at least a c/log k fraction of the optimal revenue.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000433.

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Date of creation: 14 Apr 2012
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Handle: RePEc:cla:levarc:786969000000000433

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  1. Manelli, Alejandro M. & Vincent, Daniel R., 2007. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly," Journal of Economic Theory, Elsevier, Elsevier, vol. 137(1), pages 153-185, November.
  2. Philippe Jehiel & Moritz Meyer-Ter-Vehn & Benny Moldovanu, 2006. "Mixed Bundling Auctions," Levine's Bibliography 122247000000001123, UCLA Department of Economics.
  3. Fang,H. & Norman,P., 2003. "To bundle or not to bundle," Working papers, Wisconsin Madison - Social Systems 18, Wisconsin Madison - Social Systems.
  4. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, Elsevier, vol. 117(2), pages 217-245, August.
  5. Manelli, Alejandro M. & Vincent, Daniel R., 2006. "Bundling as an optimal selling mechanism for a multiple-good monopolist," Journal of Economic Theory, Elsevier, Elsevier, vol. 127(1), pages 1-35, March.
  6. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, Elsevier, vol. 46(2), pages 335-354, December.
  7. repec:rje:randje:v:37:y:2006:i:4:p:946-963 is not listed on IDEAS
  8. Lev, Omer, 2011. "A two-dimensional problem of revenue maximization," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 718-727.
  9. Yannis Bakos & Erik Brynjolfsson, 1997. "Bundling Information Goods: Pricing, Profits and Efficiency," Working Paper Series, MIT Center for Coordination Science 199, MIT Center for Coordination Science.
  10. Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
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Cited by:
  1. Sergiu Hart & Philip J. Reny, 2012. "Maximal Revenue with Multiple Goods: Nonmonotonicity and Other Observations," Levine's Working Paper Archive 786969000000000625, David K. Levine.

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