IDEAS home Printed from https://ideas.repec.org/p/tor/tecipa/tecipa-342.html
   My bibliography  Save this paper

Budget-Constrained Sequential Auctions with Incomplete Information

Author

Listed:
  • Carolyn Pitchik

Abstract

I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder's type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α are higher when good α is sold first.

Suggested Citation

  • Carolyn Pitchik, 2008. "Budget-Constrained Sequential Auctions with Incomplete Information," Working Papers tecipa-342, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-342
    as

    Download full text from publisher

    File URL: https://www.economics.utoronto.ca/public/workingPapers/tecipa-342.pdf
    File Function: Main Text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    2. Steven M. Fazzari & Bruce C. Petersen, 1993. "Working Capital and Fixed Investment: New Evidence on Financing Constraints," RAND Journal of Economics, The RAND Corporation, vol. 24(3), pages 328-342, Autumn.
    3. Jane Black & David de Meza, 1992. "Systematic Price Differences Between Successive Auctionsare no Anomaly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 1(4), pages 607-628, December.
    4. Archishman Chakraborty & Nandini Gupta & Rick Harbaugh, 2006. "Best foot forward or best for last in a sequential auction?," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 176-194, March.
    5. Jeremy Bulow & Paul Klemperer, 2002. "Prices and the Winner's Curse," RAND Journal of Economics, The RAND Corporation, vol. 33(1), pages 1-21, Spring.
    6. Gale, Ian L. & Stegeman, Mark, 2001. "Sequential Auctions of Endogenously Valued Objects," Games and Economic Behavior, Elsevier, vol. 36(1), pages 74-103, July.
    7. Bernhardt, Dan & Scoones, David, 1994. "A Note on Sequential Auctions," American Economic Review, American Economic Association, vol. 84(3), pages 653-657, June.
    8. 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.
    9. 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.
    10. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    11. Gale Ian L. & Hausch Donald B., 1994. "Bottom-Fishing and Declining Prices in Sequential Auctions," Games and Economic Behavior, Elsevier, vol. 7(3), pages 318-331, November.
    12. Engelbrecht-Wiggans, R. & Menezes, F., 1993. "Sequential Auction with Continuation Costs," Papers 255, Australian National University - Department of Economics.
    13. 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.
    14. Gian Luca Clementi & Hugo A. Hopenhayn, 2006. "A Theory of Financing Constraints and Firm Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 121(1), pages 229-265.
    15. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
    16. Menezes, F.M., 1993. "Ascending-Price Multiple-Object Auctions," Papers 254, Australian National University - Department of Economics.
    17. Kala Krishna, 1999. "Auctions with endogenous valuations: the snowball effect revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 377-391.
    18. Inessa Love, 2003. "Financial Development and Financing Constraints: International Evidence from the Structural Investment Model," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 765-791, July.
    19. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    20. Pitchik, Carolyn, 2009. "Budget-constrained sequential auctions with incomplete information," Games and Economic Behavior, Elsevier, vol. 66(2), pages 928-949, July.
    21. Menezes, Flavio M., 1996. "Multiple-unit English auctions," European Journal of Political Economy, Elsevier, vol. 12(4), pages 671-684, December.
    22. Ashenfelter, Orley & Genesove, David, 1992. "Testing for Price Anomalies in Real-Estate Auctions," American Economic Review, American Economic Association, vol. 82(2), pages 501-505, May.
    23. Gian Luca Clementi & Hugo Hopenhayn, "undated". "A Theory of Financing Constraints and Firm Dynamics," GSIA Working Papers 2002-E9, Carnegie Mellon University, Tepper School of Business.
    24. Harris, Milton & Raviv, Artur, 1981. "Allocation Mechanisms and the Design of Auctions," Econometrica, Econometric Society, vol. 49(6), pages 1477-1499, November.
    25. Steven M. Fazzari & R. Glenn Hubbard & Bruce C. Petersen, 1988. "Financing Constraints and Corporate Investment," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 19(1), pages 141-206.
    26. 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.
    27. Peter C. Cramton, 1995. "Money Out of Thin Air: The nationwide Narrowband pcs Auction," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(2), pages 267-343, June.
    28. Gale, I. & Hausch, D., 1992. "Bottom-Fishing and Declining Prices in Sequential Auctions," Working papers 9215, Wisconsin Madison - Social Systems.
    29. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    30. Swinkels, J., 1990. "Multi-Unit, Multi-Period Auctions. Supply Uncertaincy Of Symetric Equilibria," Papers 115, Princeton, Department of Economics - Financial Research Center.
    31. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    32. Leininger, W. & Linhart, P. B. & Radner, R., 1989. "Equilibria of the sealed-bid mechanism for bargaining with incomplete information," Journal of Economic Theory, Elsevier, vol. 48(1), pages 63-106, June.
    33. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    34. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    35. Roberto Burguet & R. McAfee, 2009. "License prices for financially constrained firms," Journal of Regulatory Economics, Springer, vol. 36(2), pages 178-198, October.
    36. Pitchik, Carolyn & Schotter, Andrew, 1986. "Budget Constrained Sequential Auctions," Working Papers 86-21, C.V. Starr Center for Applied Economics, New York University.
    37. Archishman Chakraborty & Nandini Gupta & Rick Harbaugh, 2006. "Best Foot Forward or Best for Last in a Sequential Auction?," RAND Journal of Economics, The RAND Corporation, vol. 37(1), pages 176-194, Spring.
    38. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
    39. Ashenfelter, Orley, 1989. "How Auctions Work for Wine and Art," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 23-36, Summer.
    40. Richard Engelbrecht-Wiggans & Robert J. Weber, 1979. "An Example of a Multi-Object Auction Game," Management Science, INFORMS, vol. 25(12), pages 1272-1277, December.
    41. Fazzari, Steven M & Athey, Michael J, 1987. "Asymmetric Information, Financing Constraints, and Investment," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 481-487, August.
    42. Hart, Oliver & Moore, John, 1995. "Debt and Seniority: An Analysis of the Role of Hard Claims in Constraining Management," American Economic Review, American Economic Association, vol. 85(3), pages 567-585, June.
    43. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    44. Lewis, Tracy R & Sappington, David E M, 1989. "Inflexible Rules in Incentive Problems," American Economic Review, American Economic Association, vol. 79(1), pages 69-84, March.
    45. Whited, Toni M, 1992. "Debt, Liquidity Constraints, and Corporate Investment: Evidence from Panel Data," Journal of Finance, American Finance Association, vol. 47(4), pages 1425-1460, September.
    46. Hendricks, Kenneth & Porter, Robert H, 1992. "Joint Bidding in Federal OCS Auctions," American Economic Review, American Economic Association, vol. 82(2), pages 506-511, May.
    47. Wedad Elmaghraby, 2003. "The Importance of Ordering in Sequential Auctions," Management Science, INFORMS, vol. 49(5), pages 673-682, May.
    48. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    49. Krishna, Kala, 1993. "Auctions with Endogenous Valuations: The Persistence of Monopoly Revisited," American Economic Review, American Economic Association, vol. 83(1), pages 147-160, March.
    50. Lewis, Tracy R. & Sappington, David E. M., 1989. "Countervailing incentives in agency problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 294-313, December.
    51. McAfee R. Preston & Vincent Daniel, 1993. "The Declining Price Anomaly," Journal of Economic Theory, Elsevier, vol. 60(1), pages 191-212, June.
    52. Robert J. Weber, 1981. "Multiple-Object Auctions," Discussion Papers 496, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    53. Genesove, David, 1993. "Adverse Selection in the Wholesale Used Car Market," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 644-665, August.
    54. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roberto Burguet & R. McAfee, 2009. "License prices for financially constrained firms," Journal of Regulatory Economics, Springer, vol. 36(2), pages 178-198, October.
    2. Roberto Burguet, 2000. "Auction theory: a guided tour," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 3-50, January.
    3. J. Reiß & Jens Schöndube, 2010. "First-price equilibrium and revenue equivalence in a sequential procurement auction model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 99-141, April.
    4. Cramton, Peter C, 1995. "Money Out of Thin Air: The Nationwide Narrowband PCS Auction," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(2), pages 267-343, Summer.
    5. Mezzetti, Claudio, 2008. "Aversion to Price Risk and the Afternoon Effect," Economic Research Papers 269855, University of Warwick - Department of Economics.
    6. Rosato, Antonio, 2014. "Loss Aversion in Sequential Auctions: Endogenous Interdependence, Informational Externalities and the "Afternoon Effect"," MPRA Paper 56824, University Library of Munich, Germany.
    7. Orley Ashenfelter & Kathryn Graddy, 2002. "Art Auctions: A Survey of Empirical Studies," Working Papers 121, Princeton University, Department of Economics, Center for Economic Policy Studies..
    8. Hon-Snir, Shlomit & Monderer, Dov & Sela, Aner, 1998. "A Learning Approach to Auctions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 65-88, September.
    9. Jofre-Bonet, Mireia & Pesendorfer, Martin, 2014. "Optimal sequential auctions," International Journal of Industrial Organization, Elsevier, vol. 33(C), pages 61-71.
    10. R. Preston McAfee & John McMillan, 1996. "Analyzing the Airwaves Auction," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 159-175, Winter.
    11. Lucio Picci & Antonello Scorcu, 2003. "Bidders' and Sellers' Strategies in Sequential Auctions. New Evidence about the Afternoon Effect," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 30(2), pages 163-178, June.
    12. Orley Ashenfelter & Kathryn Graddy, 2003. "Auctions and the Price of Art," Journal of Economic Literature, American Economic Association, vol. 41(3), pages 763-787, September.
    13. Laffont, Jean-Jacques, 1997. "Game theory and empirical economics: The case of auction data 1," European Economic Review, Elsevier, vol. 41(1), pages 1-35, January.
    14. Gerard J. van den Berg & Jan C. van Ours & Menno P. Pradhan, 2001. "The Declining Price Anomaly in Dutch Dutch Rose Auctions," American Economic Review, American Economic Association, vol. 91(4), pages 1055-1062, September.
    15. Tibor Neugebauer & Paul Pezanis-Christou, 2003. "Bidding at Sequential First-Price Auctions with(out) Supply Uncertainty: A Laboratory Analysis," UFAE and IAE Working Papers 558.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    16. Tibor Neugebauer, 2005. "Bidding Strategies Of Sequential First Price Auctions Programmed By Experienced Bidders," Experimental 0503007, University Library of Munich, Germany.
    17. Jean-Jacques Laffont, 1998. "Théorie des jeux et économie empirique : le cas des données issues d'enchères," Économie et Prévision, Programme National Persée, vol. 132(1), pages 121-137.
    18. Ronald M. Harstad, 2007. "Does a Seller Really Want Another Bidder?," Working Papers 0711, Department of Economics, University of Missouri.
    19. Axel Ockenfels & David Reiley & Abdolkarim Sadrieh, 2006. "Online Auctions," NBER Working Papers 12785, National Bureau of Economic Research, Inc.
    20. Lawrence M. Ausubel & Peter Cramton & Marek Pycia & Marzena Rostek & Marek Weretka, 2014. "Demand Reduction and Inefficiency in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1366-1400.

    More about this item

    Keywords

    sequential auctions; budget constraints; efficiency; revenue; price; sequence;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

    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:tor:tecipa:tecipa-342. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: RePEc Maintainer (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.