IDEAS home Printed from https://ideas.repec.org/p/yor/yorken/11-04.html
   My bibliography  Save this paper

An Ascending Multi-Item Auction with Financially Constrained Bidders

Author

Listed:
  • Gerard van der Laan
  • Zaifu Yang

Abstract

A number of heterogeneous items are to be sold to a group of potential bidders. Every bidder knows his own values over the items and his own budget privately. Due to budget constraint, bidders may not be able to pay up to their values. In such a market, a Walrasian equilibrium typically fails to exist and furthermore no existing allocation mechanism can tackle this case. We propose the notion of an `equilibrium under allotment' to such markets and develop an ascending auction mechanism that always finds such an equilibrium assignment and corresponding price system in finitely many rounds. The auction can be viewed as an appropriate and proper generalization of the ascending auction of Demange, Gale and Sotomayor from settings without financial constraints to settings with financial constraints. We examine various properties of the auction and its outcome.

Suggested Citation

  • Gerard van der Laan & Zaifu Yang, 2011. "An Ascending Multi-Item Auction with Financially Constrained Bidders," Discussion Papers 11/04, Department of Economics, University of York.
  • Handle: RePEc:yor:yorken:11/04
    as

    Download full text from publisher

    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2011/1104.pdf
    File Function: Main text
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Pitchik, Carolyn & Schotter, Andrew, 1986. "Budget Constrained Sequential Auctions," Working Papers 86-21, C.V. Starr Center for Applied Economics, New York University.
    2. Andersson, Tommy & Yang, Zaifu & Zhang, Dongmo, 2015. "How to efficiently allocate houses under price controls?," Economics Letters, Elsevier, vol. 130(C), pages 97-99.
    3. Sandro Brusco & Giuseppe Lopomo, 2002. "Simultaneous Ascending Bid Auctions with Budget Constraints," Working Papers 02-14, New York University, Leonard N. Stern School of Business, Department of Economics.
    4. T. Andersson & C. Andersson & A. Talman, 2013. "Sets in excess demand in simple ascending auctions with unit-demand bidders," Annals of Operations Research, Springer, vol. 211(1), pages 27-36, December.
    5. Sandro Brusco & Giuseppe Lopomo, 2009. "Simultaneous ascending auctions with complementarities and known budget constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 105-124, January.
    6. David J. Salant, 1997. "Up in the Air: GTE's Experience in the MTA Auction for Personal Communication Services Licenses," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(3), pages 549-572, September.
    7. Andersson, Tommy & Svensson, Lars-Gunnar, 2016. "Strategy-proof house allocation with price restrictions," Journal of Economic Theory, Elsevier, vol. 163(C), pages 167-177.
    8. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    9. Herings, P. Jean-Jacques & Konovalov, Alexander, 2009. "Constrained suboptimality when prices are non-competitive," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 43-58, January.
    10. repec:jmi:articl:jmi-v1i1a4 is not listed on IDEAS
    11. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    12. Talman, Dolf & Yang, Zaifu, 2008. "A dynamic auction for differentiated items under price rigidities," Economics Letters, Elsevier, vol. 99(2), pages 278-281, May.
    13. van der Laan, Gerard, 1980. "Equilibrium under Rigid Prices with Compensation for the consumers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 63-73, February.
    14. Sotomayor, Marilda, 2002. "A Simultaneous Descending Bid Auction for Multiple Items and Unitary Demand," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 56(3), July.
    15. Pitchik, Carolyn, 2009. "Budget-constrained sequential auctions with incomplete information," Games and Economic Behavior, Elsevier, vol. 66(2), pages 928-949, July.
    16. Sandro Brusco & Giuseppe Lopomo, 2008. "BUDGET CONSTRAINTS AND DEMAND REDUCTION IN SIMULTANEOUS ASCENDING-BID AUCTIONS -super-," Journal of Industrial Economics, Wiley Blackwell, vol. 56(1), pages 113-142, March.
    17. Jean-Pierre Benoît & Vijay Krishna, 2001. "Multiple-Object Auctions with Budget Constrained Bidders," Review of Economic Studies, Oxford University Press, vol. 68(1), pages 155-179.
    18. Mishra, D. & Talman, A.J.J., 2006. "Overdemand and Underdemand in Economies with Indivisible Goods and Unit Demands," Discussion Paper 2006-84, Tilburg University, Center for Economic Research.
    19. Carolyn Pitchik & Andrew Schotter, 1988. "Perfect Equilibria in Budget-Constrained Sequential Auctions: An Experimental Study," RAND Journal of Economics, The RAND Corporation, vol. 19(3), pages 363-388, Autumn.
    20. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    21. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    22. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    23. Zheng, Charles Z., 2001. "High Bids and Broke Winners," Journal of Economic Theory, Elsevier, vol. 100(1), pages 129-171, September.
    24. Yeon-Koo Che & Ian Gale, 1998. "Standard Auctions with Financially Constrained Bidders," Review of Economic Studies, Oxford University Press, vol. 65(1), pages 1-21.
    25. Thomas R. Palfrey, 1980. "Multiple-Object, Discriminatory Auctions with Bidding Constraints: A Game-Theoretic Analysis," Management Science, INFORMS, vol. 26(9), pages 935-946, September.
    26. Ning Sun & Zaifu Yang, 2009. "A Double-Track Adjustment Process for Discrete Markets With Substitutes and Complements," Econometrica, Econometric Society, vol. 77(3), pages 933-952, May.
    27. 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.
    28. Herings P.J.J., 2015. "Equilibrium and matching under price controls," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    29. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
    30. Gerard van der Laan & Zaifu Yang, 2016. "An ascending multi-item auction with financially constrained bidders," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 109-149, December.
    31. Michael H. Rothkopf, 1977. "Bidding in Simultaneous Auctions with a Constraint on Exposure," Operations Research, INFORMS, vol. 25(4), pages 620-629, August.
    32. Ning Sun & Zaifu Yang, 2014. "An Efficient and Incentive Compatible Dynamic Auction for Multiple Complements," Discussion Papers 14/06, Department of Economics, University of York.
    33. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    34. Tommy Andersson & Lars‐Gunnar Svensson, 2014. "Non‐Manipulable House Allocation With Rent Control," Econometrica, Econometric Society, vol. 82(2), pages 507-539, March.
    35. 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.
    36. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andersson, Tommy & Yang, Zaifu & Zhang, Dongmo, 2015. "How to efficiently allocate houses under price controls?," Economics Letters, Elsevier, vol. 130(C), pages 97-99.
    2. Gerard van der Laan & Zaifu Yang, 2016. "An ascending multi-item auction with financially constrained bidders," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 109-149, December.

    More about this item

    Keywords

    Ascending auction; Financial constraint; Equilibrium under allotment.;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:yor:yorken:11/04. 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: (Paul Hodgson). General contact details of provider: http://edirc.repec.org/data/deyoruk.html .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.