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Auctions with Dynamic Populations: Efficiency and Revenue Maximization

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  • Said, Maher

Abstract

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11456.

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Date of creation: 19 Nov 2008
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Handle: RePEc:pra:mprapa:11456

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Related research

Keywords: Dynamic mechanism design; Random arrivals; Revenue equivalence; Indirect mechanisms; Sequential ascending auctions;

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References

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  1. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, EconWPA, revised 28 Apr 1998.
  2. 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.
  3. 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.
  4. Mallesh Pai & Rakesh Vohra, 2008. "Optimal Dynamic Auctions," Discussion Papers 1461, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Gershkov, Alex & Moldovanu, Benny, 2010. "Efficient sequential assignment with incomplete information," Games and Economic Behavior, Elsevier, vol. 68(1), pages 144-154, January.
  6. 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.
  7. 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.
  8. 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.
  9. Dirk Bergemann & Juuso Valimaki, 2008. "The Dynamic Pivot Mechanism," Cowles Foundation Discussion Papers 1672, Cowles Foundation for Research in Economics, Yale University.
  10. 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.
  11. Said, Maher, 2008. "Information Revelation and Random Entry in Sequential Ascending Auctions," MPRA Paper 7160, University Library of Munich, Germany.
  12. Robert J. Dolan, 1978. "Incentive Mechanisms for Priority Queuing Problems," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 421-436, Autumn.
  13. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Susan Athey & Ilya Segal, 2007. "An Efficient Dynamic Mechanism," Levine's Bibliography 122247000000001134, UCLA Department of Economics.
  15. 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.
  16. 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.
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Cited by:
  1. Dirk Bergemann & Maher Said, 2010. "Dynamic Auctions: A Survey," Levine's Working Paper Archive 661465000000000035, David K. Levine.

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