Approximate Revenue Maximization with Multiple Items
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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- Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
- 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.
- 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.
- Hanming Fang & Peter Norman, 2006. "To bundle or not to bundle," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 946-963, December.
- Fang,H. & Norman,P., 2003. "To bundle or not to bundle," Working papers 18, Wisconsin Madison - Social Systems.
- Hanming Fang & Peter Norman, 2003. "To Bundle or Not to Bundle," Cowles Foundation Discussion Papers 1440, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Jehiel, Philippe & Meyer-ter-Vehn, Moritz & Moldovanu, Benny, 2007. "Mixed bundling auctions," Journal of Economic Theory, Elsevier, vol. 134(1), pages 494-512, May.
- Philippe Jehiel & Moritz Meyer-Ter-Vehn & Benny Moldovanu, 2006. "Mixed Bundling Auctions," Levine's Bibliography 122247000000001123, UCLA Department of Economics.
- Jehiel, Philippe & Meyer-Ter-Vehn, Moritz & Moldovanu, Benny, 2006. "Mixed Bundling Auctions," CEPR Discussion Papers 5566, C.E.P.R. Discussion Papers.
- Philippe Jehiel & Moritz Meyer-Ter-Vehn & Benny Moldovanu, 2007. "Mixed Bundling Auctions," Post-Print halshs-00754233, HAL.
- 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.
- Yannis Bakos & Erik Brynjolfsson, 1999. "Bundling Information Goods: Pricing, Profits, and Efficiency," Management Science, INFORMS, vol. 45(12), pages 1613-1630, December.
- Yannis Bakos & Erik Brynjolfsson, 1997. "Bundling Information Goods: Pricing, Profits and Efficiency," Working Paper Series 199, MIT Center for Coordination Science.
- repec:rje:randje:v:37:y:2006:i:4:p:946-963 is not listed on IDEAS
- Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
- Lev, Omer, 2011. "A two-dimensional problem of revenue maximization," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 718-727.
- McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
- 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. Full references (including those not matched with items on IDEAS)