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Comparing Competition and Collusion in Procurement Auctions: A Numerical Approach

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Patrick Bajari
Abstract

January 2000, Revised January 2001

Collusion is a serious problem in many procurement auctions. In this research, I study a model of first price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging.

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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 00003.

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  1. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June. [Downloadable!] (restricted)
  2. Porter, Robert H & Zona, J Douglas, 1993. "Detection of Bid Rigging in Procurement Auctions," Journal of Political Economy, University of Chicago Press, vol. 101(3), pages 518-38, June. [Downloadable!] (restricted)
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  3. Bernard Lebrun, 1996. "Existence of an equilibrium in first price auctions (*)," Economic Theory, Springer, vol. 7(3), pages 421-443.
  4. Robert H. Porter & J. Douglas Zona, 1999. "Ohio School Milk Markets: An Analysis of Bidding," RAND Journal of Economics, The RAND Corporation, vol. 30(2), pages 263-288, Summer. [Downloadable!] (restricted)
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  5. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September. [Downloadable!] (restricted)
  6. Laffont, Jean-Jacques & Ossard, Hervé & Vuong, Quang, 1991. "Econometrics of First-Price Auctions," IDEI Working Papers 7, Institut d'Économie Industrielle (IDEI), Toulouse.
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  7. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 413-38, July.
  8. Lebrun, Bernard, 1996. "Existence of an Equilibrium in First Price Auctions," Economic Theory, Springer, vol. 7(3), pages 421-43, April.
  9. Alessandro Lizzeri & Nicola Persico, 1995. "Existence and Uniqueness of Equilibrium In First Place Auctions and War of Attrition with Affiliated Values," Discussion Papers 1120, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  10. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
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  11. Pesendorfer, Martin, 2000. "A Study of Collusion in First-Price Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 381-411, July.
  12. Estelle Cantillon, 2000. "The Effect of Bidders' Asymmetries on Expected Revenue in Auctions," Cowles Foundation Discussion Papers 1279, Cowles Foundation, Yale University. [Downloadable!]
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  13. Armantier, O. & Florens, J.-P. & Richard, J.-F., 1998. "Empirical Game Theoretic Models: Constrained Equilibrium & Simulation," Papers 98.498, Toulouse - GREMAQ.
  14. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September. [Downloadable!] (restricted)
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