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Bertrand Competition Under Uncertainty

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  • Eric Rasmusen

    (Indiana University School of Business)

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 simple 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 do decline more sharply than in the Cournot model, and the pattern is similar to that found by Bresnahan and Reiss (1991).

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Paper provided by EconWPA in its series Industrial Organization with number 9607002.

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Date of creation: 20 Jul 1996
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Handle: RePEc:wpa:wuwpio:9607002

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  1. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  2. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 27-41, January.
  3. 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.
  4. Salop, Steven & Stiglitz, Joseph E, 1977. "Bargains and Ripoffs: A Model of Monopolistically Competitive Price Dispersion," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 493-510, October.
  5. 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.
  6. 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.
  7. 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.
  8. Elmar Wolfstetter & Walter Elberfeld, 1997. "A Dynamic Model of Bertrand Competition with Entry," Microeconomics 9701003, EconWPA.
  9. Gaudet, G. & Salant, S.W., 1988. "Uniqueness Of Cournot Equilibrium: New Results From Old Methods," Cahiers de recherche 8818, Université Laval - Département d'économique.
  10. Kevin Lang & Robert W. Rosenthal, 1991. "The Contractors' Game," RAND Journal of Economics, The RAND Corporation, vol. 22(3), pages 329-338, Autumn.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
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Cited by:
  1. Johannes Münster, 2006. "Contests with an unknown number of contestants," Public Choice, Springer, vol. 129(3), pages 353-368, December.
  2. 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.
  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. 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.
  5. 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.
  6. Michael R. Baye & John Morgan, 2009. "Brand and Price Advertising in Online Markets," Management Science, INFORMS, vol. 55(7), pages 1139-1151, July.
  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. Jellal, Mohamed & wolff, François charles, 2005. "Free entry under uncertainty," MPRA Paper 38376, University Library of Munich, Germany.
  9. 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.
  10. Michael R. Baye & John Morgan, 2005. "Probabilistic Patents," Microeconomics 0504004, EconWPA.
  11. Ritzberger, Klaus, 2009. "Price competition with population uncertainty," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 145-157, September.
  12. 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.
  13. repec:dgr:uvatin:2007081 is not listed on IDEAS

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