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Bertrand Competition Under Uncertainty

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Author Info
Maarten Janssen (Department of Economics, Erasmus University)
Eric Rasmusen (CIRJE, Faculty of Economics, University of Tokyo and Kelley School of Business, Indiana University)

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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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Publisher 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
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Handle: RePEc:tky:fseres:2001cf117

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  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July. [Downloadable!] (restricted)
  4. Warner, Elizabeth J & Barsky, Robert B, 1995. "The Timing and Magnitude of Retail Store Markdowns: Evidence from Weekends and Holidays," The Quarterly Journal of Economics, MIT Press, vol. 110(2), pages 321-52, May. [Downloadable!] (restricted)
  5. Salop, Steven & Stiglitz, Joseph E, 1977. "Bargains and Ripoffs: A Model of Monopolistically Competitive Price Dispersion," Review of Economic Studies, Blackwell Publishing, vol. 44(3), pages 493-510, October. [Downloadable!] (restricted)
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  6. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Blackwell Publishing, vol. 53(1), pages 27-41, January. [Downloadable!] (restricted)
  7. Kevin Lang & Robert W. Rosenthal, 1991. "The Contractors' Game," RAND Journal of Economics, The RAND Corporation, vol. 22(3), pages 329-338, Autumn. [Downloadable!] (restricted)
  8. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Blackwell Publishing, vol. 43(1), pages 1-11, March. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
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  10. Kotaro Suzumura, 1993. "Competition, Commitment and Welfare," Discussion Paper Series a269, Institute of Economic Research, Hitotsubashi University.
  11. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-22, February. [Downloadable!] (restricted)
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  12. Janssen, Maarten C. W. & van Reeven, Peran, 1998. "Market Prices and Illegal Practices," International Review of Law and Economics, Elsevier, vol. 18(1), pages 51-60, March. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
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  14. Gaudet, Gerard & Salant, Stephen W, 1991. "Uniqueness of Cournot Equilibrium: New Results from Old Methods," Review of Economic Studies, Blackwell Publishing, vol. 58(2), pages 399-404, April. [Downloadable!] (restricted)
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  15. 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. [Downloadable!] (restricted)
  16. Chantale LaCasse, 1995. "Bid Rigging and the Threat of Government Prosecution," RAND Journal of Economics, The RAND Corporation, vol. 26(3), pages 398-417, Autumn. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Johannes Münster, 2006. "Contests with an unknown number of contestants," Public Choice, Springer, vol. 129(3), pages 353-368, December. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  3. Mohamed Jellal & François-Charles Wolff, 2005. "Free Entry under Uncertainty," Journal of Economics, Springer, vol. 85(1), pages 39-63, 07. [Downloadable!] (restricted)
  4. 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. [Downloadable!]
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  5. Michael R. Baye & John Morgan, 2005. "Probabilistic Patents," Microeconomics 0504004, EconWPA. [Downloadable!]
  6. Maarten C.W. Janssen & Santanu Roy, 2007. "Signaling Quality Through Prices in an Oligopoly," Departmental Working Papers 0709, Southern Methodist University, Department of Economics, revised Nov 2008. [Downloadable!]
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  7. Halevy, Yoram & Michtaich, Igal, 2005. "Poisson Price Dispersion," Micro Theory Working Papers halevy-05-07-26-12-10-45, Microeconomics.ca Website, revised 08 Jun 2008. [Downloadable!]
  8. Alfredo Martín-Oliver & Vicente Salas-Fumás & Jesús Saurina, 2005. "Interest rate dispersion in deposit and loan markets," Banco de España Working Papers 0506, Banco de España. [Downloadable!]
  9. 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. [Downloadable!]
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