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.
|Date of creation:||18 Apr 2012|
|Date of revision:|
|Contact details of provider:|| Postal: Feldman Building - Givat Ram - 91904 Jerusalem|
Web page: http://www.ratio.huji.ac.il/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hanming Fang & Peter Norman, 2006.
"To bundle or not to bundle,"
RAND Journal of Economics,
RAND Corporation, vol. 37(4), pages 946-963, December.
- 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.
- Fang,H. & Norman,P., 2003. "To bundle or not to bundle," Working papers 18, Wisconsin Madison - Social Systems.
- Yannis Bakos & Erik Brynjolfsson, 1999.
"Bundling Information Goods: Pricing, Profits, and Efficiency,"
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.
- 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.
- Philippe Jehiel & Moritz Meyer-Ter-Vehn & Benny Moldovanu, 2006. "Mixed Bundling Auctions," Levine's Bibliography 122247000000001123, UCLA Department of Economics.
- Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
- 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.
- McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
- repec:rje:randje:v:37:y:2006:i:4:p:946-963 is not listed on IDEAS
- Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
- 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.
- Lev, Omer, 2011. "A two-dimensional problem of revenue maximization," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 718-727.
When requesting a correction, please mention this item's handle: RePEc:huj:dispap:dp606. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ilan Nehama)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.