IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

Multi-unit auctions with budget limits

  • Dobzinski, Shahar
  • Lavi, Ron
  • Nisan, Noam

We study multi-unit auctions for bidders that have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there is no deterministic auction that (1) is individually rational and dominant-strategy incentive-compatible, (2) makes no positive transfers, and (3) always produces a Pareto optimal outcome. In contrast, we show that Ausubelʼs “clinching auction” satisfies all these properties when the budgets are public knowledge. Moreover, we prove that the “clinching auction” is the unique auction that satisfies all these properties when there are two players. This uniqueness result is the cornerstone of the impossibility result. Few additional related results are given, including some results on the revenue of the clinching auction and on the case where the items are divisible.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 74 (2012)
Issue (Month): 2 ()
Pages: 486-503

in new window

Handle: RePEc:eee:gamebe:v:74:y:2012:i:2:p:486-503
Contact details of provider: Web page:

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.:

as in new window
  1. Kagel, John H & Levin, Dan, 2001. "Behavior in Multi-unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions," Econometrica, Econometric Society, vol. 69(2), pages 413-54, March.
  2. Mallesh M. Pai & Rakesh Vohra, 2008. "Optimal Auctions with Financially Constrained Bidders," Discussion Papers 1471, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  4. repec:oup:restud:v:68:y:2001:i:1:p:155-79 is not listed on IDEAS
  5. Ashlagi Itai & Braverman Mark & Hassidim Avinatan & Lavi Ron & Tennenholtz Moshe, 2010. "Position Auctions with Budgets: Existence and Uniqueness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-32, May.
  6. Goldberg, Andrew V. & Hartline, Jason D. & Karlin, Anna R. & Saks, Michael & Wright, Andrew, 2006. "Competitive auctions," Games and Economic Behavior, Elsevier, vol. 55(2), pages 242-269, May.
  7. Sandro Brusco & Giuseppe Lopomo, 2004. "Simultaneous Ascending Bid Auctions with Privately Known Budget Constraints," Levine's Bibliography 122247000000000373, UCLA Department of Economics.
  8. repec:oup:restud:v:65:y:1998:i:1:p:1-21 is not listed on IDEAS
  9. Mishra, Debasis & Parkes, David C., 2009. "Multi-item Vickrey-Dutch auctions," Games and Economic Behavior, Elsevier, vol. 66(1), pages 326-347, May.
  10. Laffont, Jean-Jacques & Robert, Jacques, 1996. "Optimal auction with financially constrained buyers," Economics Letters, Elsevier, vol. 52(2), pages 181-186, August.
  11. 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.
  12. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," ULB Institutional Repository 2013/99376, ULB -- Universite Libre de Bruxelles.
  13. John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer, vol. 33(3), pages 505-515, September.
  14. Motty Perry & Philip J. Reny, 2005. "An Efficient Multi-Unit Ascending Auction," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 567-592.
  15. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  16. Sushil Bikhchandani & Shurojit Chatterji & Ron Lavi & Ahuva Mu'alem & Noam Nisan & Arunava Sen, 2006. "Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1109-1132, 07.
  17. Maskin, Eric S., 2000. "Auctions, development, and privatization: Efficient auctions with liquidity-constrained buyers," European Economic Review, Elsevier, vol. 44(4-6), pages 667-681, May.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:74:y:2012:i:2:p:486-503. 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: (Zhang, Lei)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.