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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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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp606.

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Length: 32 pages
Date of creation: 18 Apr 2012
Date of revision:
Handle: RePEc:huj:dispap:dp606

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  1. 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.
  2. repec:rje:randje:v:37:y:2006:i:4:p:946-963 is not listed on IDEAS
  3. Fang, Hanming & Norman, Peter, 2005. "To Bundle or Not to Bundle," Microeconomics.ca working papers norman-05-06-10-08-19-02, Vancouver School of Economics, revised 10 Jun 2005.
  4. Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
  5. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
  6. Jehiel, Philippe & Meyer-ter-Vehn, Moritz & Moldovanu, Benny, 2006. "Mixed Bundling Auctions," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 141, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  7. 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.
  8. Yannis Bakos & Erik Brynjolfsson, 1997. "Bundling Information Goods: Pricing, Profits and Efficiency," Working Paper Series 199, MIT Center for Coordination Science.
  9. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
  10. 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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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.

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