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Bertrand Competition under Uncertainty

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  • Maarten C.W. Janssen

    ()
    (Erasmus University Rotterdam)

  • Eric Rasmusen

    ()
    (Indiana University)

Abstract

Consider a Bertrand model in which each firm may be inactive with aknown probability, so the number of active firms is uncertain. Thissimple model has a mixed-strategy equilibrium in which industryprofits are positive and decline with the number of firms, the samefeatures which make the Cournot model attractive. Unlike in a Cournotmodel with similar incomplete information, Bertrand profits alwaysncrease in the probability other firms are inactive. Profits declinemore sharply than in the Cournot model, and the pattern is similar tothat found by Bresnahan & Reiss (1991).

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 98-083/1.

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Date of creation: 18 Aug 1998
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Handle: RePEc:dgr:uvatin:19980083

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References

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  1. Bresnahan, T.F & Reiss, P.C., 1989. "Entry And Competition In Concentrated Markets," Papers 151, Stanford - Studies in Industry Economics.
  2. Gaudet, G. & Salant, S.W., 1988. "Uniqueness Of Cournot Equilibrium: New Results From Old Methods," Cahiers de recherche 8818, Université Laval - Département d'économique.
  3. Elmar Wolfstetter & Walter Elberfeld, 1997. "A Dynamic Model of Bertrand Competition with Entry," Microeconomics 9701003, EconWPA.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Kevin Lang & Robert W. Rosenthal, 1991. "The Contractors' Game," RAND Journal of Economics, The RAND Corporation, vol. 22(3), pages 329-338, Autumn.
  9. Richard E. Levitan & Martin Shubik, 1970. "Price Duopoly and Capacity Constraints," Cowles Foundation Discussion Papers 287, Cowles Foundation for Research in Economics, Yale University.
  10. 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.
  11. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
  12. Steven Salop & Joseph Stiglitz, 1977. "Bargains and ripoffs: a model of monopolistically competitive price dispersion," Special Studies Papers 94, Board of Governors of the Federal Reserve System (U.S.).
  13. 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.
  14. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  15. 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.
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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. Eric B. Rasmusen, 2001. "Starategic Implications of Uncertainty Over One's Own Private Value in Auctions," CIRJE F-Series CIRJE-F-127, CIRJE, Faculty of Economics, University of Tokyo.
  3. Baye, Michael & Morgan, John, 2004. "Brand and Price Advertising in Online Markets," Competition Policy Center, Working Paper Series qt9760k3hz, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley.
  4. 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.
  5. repec:dgr:uvatin:2007081 is not listed on IDEAS
  6. 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.
  7. Mohamed Jellal & François-Charles Wolff, 2005. "Free Entry under Uncertainty," Journal of Economics, Springer, vol. 85(1), pages 39-63, 07.
  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. Johannes Münster, 2006. "Contests with an unknown number of contestants," Public Choice, Springer, vol. 129(3), pages 353-368, December.
  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. Michael R. Baye & John Morgan, 2005. "Probabilistic Patents," Microeconomics 0504004, EconWPA.
  12. 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.
  13. Ritzberger, Klaus, 2009. "Price competition with population uncertainty," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 145-157, September.

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