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Uniqueness of the equilibrium in first-price auctions

  • Lebrun, Bernard

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

Volume (Year): 55 (2006)
Issue (Month): 1 (April)
Pages: 131-151

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Handle: RePEc:eee:gamebe:v:55:y:2006:i:1:p:131-151
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. 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.
  2. Kenneth Hendricks & Robert Porter, 1989. "Collusion in Auctions," Discussion Papers 817, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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. 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.
  5. 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.
  6. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
  7. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  8. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers 152, UCLA Department of Economics.
  9. An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers 95-03, Duke University, Department of Economics.
  10. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
  11. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-42, February.
  12. Thomas, Charles J., 1997. "Disincentives for cost-reducing investment," Economics Letters, Elsevier, vol. 57(3), pages 359-363, December.
  13. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
  14. 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.
  15. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
  16. 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.
  17. Marshall, R.C. & Richard J.F., 1995. "Bider Collusion at Forest Service Timber Sales," Papers 7-95-3, Pennsylvania State - Department of Economics.
  18. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
  19. 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.
  20. 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.
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