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Bertrand Competition Under Uncertainty


  • Maarten Janssen

    (Department of Economics, Erasmus University)

  • Eric Rasmusen

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


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).

Suggested Citation

  • Maarten Janssen & Eric Rasmusen, 2001. "Bertrand Competition Under Uncertainty," CIRJE F-Series CIRJE-F-117, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2001cf117

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    Cited by:

    1. Janssen, Maarten C.W. & Roy, Santanu, 2010. "Signaling quality through prices in an oligopoly," Games and Economic Behavior, Elsevier, vol. 68(1), pages 192-207, January.
    2. Rasmusen Eric Bennett, 2006. "Strategic Implications of Uncertainty over One's Own Private Value in Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-22, November.
    3. Michael R. Baye & John Morgan, 2009. "Brand and Price Advertising in Online Markets," Management Science, INFORMS, vol. 55(7), pages 1139-1151, July.
    4. Ritzberger, Klaus, 2009. "Price competition with population uncertainty," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 145-157, September.
    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. Paul Belleflamme & Wing Man Wynne Lam & Wouter Vergote, 2017. "Price Discrimination and Dispersion under Asymmetric Profiling of Consumers," Working Papers halshs-01502452, HAL.
    7. Ashish Arora & Amy Greenwald & Karthik Kannan & Ramayya Krishnan, 2007. "Effects of Information-Revelation Policies Under Market-Structure Uncertainty," Management Science, INFORMS, vol. 53(8), pages 1234-1248, August.
    8. Mohamed Jellal & François-Charles Wolff, 2005. "Free Entry under Uncertainty," Journal of Economics, Springer, vol. 85(1), pages 39-63, July.
    9. Charles J. Thomas, 2010. "INFORMATION REVELATION AND BUYER PROFITS IN REPEATED PROCUREMENT COMPETITION -super-," Journal of Industrial Economics, Wiley Blackwell, vol. 58(1), pages 79-105, March.
    10. 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.
    11. 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.
    12. Johannes Münster, 2006. "Contests with an unknown number of contestants," Public Choice, Springer, vol. 129(3), pages 353-368, December.
    13. Michael R. Baye & John Morgan, 2005. "Probabilistic Patents," Microeconomics 0504004, EconWPA.
    14. Guha, Brishti, 2016. "Moral Hazard, Bertrand Competition, and Natural Monopoly," MPRA Paper 70966, University Library of Munich, Germany.
    15. Charles Thomas, 2011. "The Price Effects of Using Firewalls as an Antitrust Remedy," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 38(2), pages 209-222, March.
    16. repec:kap:jeczfn:v:121:y:2017:i:2:d:10.1007_s00712-017-0527-7 is not listed on IDEAS
    17. Alfredo Martín-Oliver & Vicente Salas-Fumás & Jesús Saurina, 2005. "Interest rate dispersion in deposit and loan markets," Working Papers 0506, Banco de España;Working Papers Homepage.
    18. Jim Y. Jin & Shinji Kobayashi, 2016. "Impact of risk aversion and countervailing tax in oligopoly," Annals of Finance, Springer, vol. 12(3), pages 393-408, December.
    19. Sarang Deo & Charles J. Corbett, 2009. "Cournot Competition Under Yield Uncertainty: The Case of the U.S. Influenza Vaccine Market," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 563-576, July.

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