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Uniqueness of the Equilibrium in First-Price Auctions

  • Bernard Lebrun

    (Department of Economics, York University)

If the value cumulative distribution functions are log-concave at the highest lower extremity of their supports, a simple geometric argument establishes the uniqueness of the equilibrium of the first-price auction in the asymmetric independent private value model.

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Paper provided by York University, Department of Economics in its series Working Papers with number 2004_2.

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Length: 48 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:yca:wpaper:2004_2
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  1. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-92, June.
  2. Mark Bagnoli & Ted Bergstrom, 2005. "Log-concave probability and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 445-469, 08.
  3. Lebrun, Bernard, 1996. "Existence of an Equilibrium in First Price Auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 421-43, April.
  4. Patrick Bajari, 2001. "Comparing competition and collusion: a numerical approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 187-205.
  5. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
  6. Dalkir, Serdar & Logan, John W. & Masson, Robert T., 2000. "Mergers in symmetric and asymmetric noncooperative auction markets: the effects on prices and efficiency," International Journal of Industrial Organization, Elsevier, vol. 18(3), pages 383-413, April.
  7. Baldwin, Laura H & Marshall, Robert C & Richard, Jean-Francois, 1997. "Bidder Collusion at Forest Service Timber Sales," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 657-99, August.
  8. Kenneth Hendricks & Robert H. Porter, 1989. "Collusion in Auctions," Annals of Economics and Statistics, GENES, issue 15-16, pages 217-230.
  9. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
  10. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
  11. Robert H. Porter & J. Douglas Zona, 1997. "Ohio School Milk Markets: An Analysis of Bidding," NBER Working Papers 6037, National Bureau of Economic Research, Inc.
  12. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
  13. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  14. Waehrer, Keith, 1999. "Asymmetric private values auctions with application to joint bidding and mergers," International Journal of Industrial Organization, Elsevier, vol. 17(3), pages 437-452, April.
  15. Bernard Lebrun, 2004. "Uniqueness of the Equilibrium in First-Price Auctions," Working Papers 2004_2, York University, Department of Economics.
  16. 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.
  17. Lebrun, Bernard, 1997. "First Price Auctions in the Asymmetric N Bidder Case," Cahiers de recherche 9715, Université Laval - Département d'économique.
  18. Thomas, Charles J., 1997. "Disincentives for cost-reducing investment," Economics Letters, Elsevier, vol. 57(3), pages 359-363, December.
  19. 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.
  20. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
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