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Bertrand Competition Under Uncertainty

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  • Maarten Janssen

    (Department of Economics, Erasmus University)

  • Eric Rasmusen

    (CIRJE, Faculty of Economics, University of Tokyo and Kelley School of Business, Indiana University)

Abstract

Consider a Bertrand model in which each firm may be inactive with a known probability, so the number of active firms is uncertain. This activity level can be endogenized in several ways ---whether to incur a fixed cost of activity, for example, or what level of output to choose. Our model has a mixed-strategy equilibrium, in which industry profits are positive and decline with the number of firms, the same features which make the Cournot model attractive. Unlike in a Cournot model with similar incomplete information, Bertrand profits always increase in the probability other firms are inactive. Profits decline more sharply than in the Cournot model, and the pattern is similar to that found empirically by Bresnahan and Reiss (1991).

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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-117.

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Length: 34 pages
Date of creation: Jun 2001
Date of revision:
Handle: RePEc:tky:fseres:2001cf117

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References

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  1. Elberfeld, Walter & Wolfstetter, Elmar, 1999. "A dynamic model of Bertrand competition with entry," International Journal of Industrial Organization, Elsevier, vol. 17(4), pages 513-525, May.
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  5. Bresnahan, Timothy F & Reiss, Peter C, 1991. "Entry and Competition in Concentrated Markets," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 977-1009, October.
  6. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
  7. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
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  11. Gaudet, Gerard & Salant, Stephen W, 1991. "Uniqueness of Cournot Equilibrium: New Results from Old Methods," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 399-404, April.
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  14. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
  15. Salant, Stephen W & Switzer, Sheldon & Reynolds, Robert J, 1983. "Losses from Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 98(2), pages 185-99, May.
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Citations

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Cited by:
  1. Maarten C.W. Janssen & Santanu Roy, 2007. "Signaling Quality through Prices in an Oligopoly," Tinbergen Institute Discussion Papers 07-081/1, Tinbergen Institute.
  2. Michael R. Baye & John Morgan, 2005. "Brand and Price Advertising in Online Markets," Working Papers 2005-08, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
  3. Thomas, Charles J., 2004. "The competitive effects of mergers between asymmetric firms," International Journal of Industrial Organization, Elsevier, vol. 22(5), pages 679-692, May.
  4. Mohamed Jellal & François-Charles Wolff, 2005. "Free Entry under Uncertainty," Journal of Economics, Springer, vol. 85(1), pages 39-63, 07.
  5. Vicki Knoblauch, 2002. "A Comparison of Two-Market Bertrand Duopoly and Two-Market Cournot Duopoly," Working papers 2002-14, University of Connecticut, Department of Economics.
  6. Ritzberger, Klaus, 2009. "Price competition with population uncertainty," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 145-157, September.
  7. Eric Rasmusen, 2004. "Strategic Implications of Uncertainty Over One’s Own Private Value in Auctions," Working Papers 2004-13, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
  8. Alfredo Martín-Oliver & Vicente Salas-Fumás & Jesús Saurina, 2005. "Interest rate dispersion in deposit and loan markets," Banco de Espa�a Working Papers 0506, Banco de Espa�a.
  9. Maarten C.W. Janssen & Santanu Roy, 2007. "Signaling Quality through Prices in an Oligopoly," Tinbergen Institute Discussion Papers 07-081/1, Tinbergen Institute.
  10. Johannes Münster, 2006. "Contests with an unknown number of contestants," Public Choice, Springer, vol. 129(3), pages 353-368, December.
  11. Michael R. Baye & John Morgan, 2005. "Probabilistic Patents," Microeconomics 0504004, EconWPA.
  12. Charles Thomas, 2011. "The Price Effects of Using Firewalls as an Antitrust Remedy," Review of Industrial Organization, Springer, vol. 38(2), pages 209-222, March.
  13. Thomas, Charles J., 2002. "The effect of asymmetric entry costs on Bertrand competition," International Journal of Industrial Organization, Elsevier, vol. 20(5), pages 589-609, May.

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