Auctions with Dynamic Populations: Efficiency and Revenue Maximization
We examine an environment where goods and privately informed buyers arrive stochastically to a market. A seller in this setting faces a sequential allocation problem with a changing population. We characterize the set of incentive compatible allocation rules and provide a generalized revenue equivalence result. In contrast to a static setting where incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object, in this dynamic setting, incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object sooner. We also characterize the set of efficient allocation rules and show that a dynamic Vickrey-Clarke-Groves mechanism is efficient and dominant strategy incentive compatible. We then derive an optimal direct mechanism. We show that the revenue-maximizing direct mechanism is a pivot mechanism with a reserve price. Finally, we consider sequential ascending auctions in this setting, both with and without a reserve price. We construct memoryless equilibrium bidding strategies in this indirect mechanism. Bidders reveal their private information in every period, yielding the same outcomes as the direct mechanisms. Thus, the sequential ascending auction is a natural institution for achieving either efficient or optimal outcomes. Interestingly, this is not the case for sequential second-price auctions, as the bids in a second-price auction do not reveal sufficient information to realize either the efficient or optimal allocation.
|Date of creation:||19 Nov 2008|
|Date of revision:|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
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.:
- Perea, Andres, 2002. "A note on the one-deviation property in extensive form games," Games and Economic Behavior, Elsevier, vol. 40(2), pages 322-338, August.
- Paul Milgrom & Robert J. Weber, 1981.
"A Theory of Auctions and Competitive Bidding,"
447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kagel, John H & Harstad, Ronald M & Levin, Dan, 1987. "Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study," Econometrica, Econometric Society, vol. 55(6), pages 1275-1304, November.
- Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, EconWPA, revised 28 Apr 1998.
- Dirk Bergemann & Juuso Valimaki, 2008.
"The Dynamic Pivot Mechanism,"
Cowles Foundation Discussion Papers
1672R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2009.
- Dirk Bergemann & Juuso Valimaki, 2008. "The Dynamic Pivot Mechanism," Cowles Foundation Discussion Papers 1672, Cowles Foundation for Research in Economics, Yale University.
- Dirk Bergemann & Juuso Välimäki, 2008. "The Dynamic Pivot Mechanism," Levine's Working Paper Archive 122247000000002340, David K. Levine.
- Jeffrey S. Banks & John O. Ledyard & David P. Porter, 1989. "Allocating Uncertain and Unresponsive Resources: An Experimental Approach," RAND Journal of Economics, The RAND Corporation, vol. 20(1), pages 1-25, Spring.
- Robert J. Dolan, 1978. "Incentive Mechanisms for Priority Queuing Problems," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 421-436, Autumn.
- Mallesh Pai & Rakesh Vohra, 2008. "Optimal Dynamic Auctions," Discussion Papers 1461, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Susan Athey & Ilya Segal, 2007.
"An Efficient Dynamic Mechanism,"
122247000000001134, UCLA Department of Economics.
- Alessandro Pavan & Ilya Segal & Juuso Toikka, 2008.
"Dynamic Mechanism Design: Incentive Compatibility, Profit Maximization and Information Disclosure,"
Carlo Alberto Notebooks
84, Collegio Carlo Alberto.
- Alessandro Pavan & Ilya Segal & Juuso Toikka, 2009. "Dynamic Mechanism Design: Incentive Compatibility, Profit Maximization and Information Disclosure," Discussion Papers 1501, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Lawrence M. Ausubel, 2004. "An Efficient Ascending-Bid Auction for Multiple Objects," American Economic Review, American Economic Association, vol. 94(5), pages 1452-1475, December.
- Said, Maher, 2008. "Information Revelation and Random Entry in Sequential Ascending Auctions," MPRA Paper 7160, University Library of Munich, Germany.
- Rothkopf, Michael H & Teisberg, Thomas J & Kahn, Edward P, 1990. "Why Are Vickrey Auctions Rare?," Journal of Political Economy, University of Chicago Press, vol. 98(1), pages 94-109, February.
- Gershkov, Alex & Moldovanu, Benny, 2010. "Efficient sequential assignment with incomplete information," Games and Economic Behavior, Elsevier, vol. 68(1), pages 144-154, January.
- Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "The One-Shot-Deviation Principle for Sequential Rationality," Games and Economic Behavior, Elsevier, vol. 12(2), pages 274-282, February.
- Alex Gershkov & Benny Moldovanu, 2009. "Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 168-98, August.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:11456. 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: (Joachim Winter)
If references are entirely missing, you can add them using this form.