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Bayesian Nash Equilibrium in ''Linear'' Cournot Models with Private Information About Cost

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  • Sjaak Hurkens

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    Abstract

    Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesian equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

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    Bibliographic Info

    Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 924.12.

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    Length: 15
    Date of creation: 03 Dec 2012
    Date of revision:
    Handle: RePEc:aub:autbar:924.12

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    Keywords: Cournot; Private Information; Bayesian Nash equilibrium;

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    1. Cramton, Peter C. & Palfrey, Thomas R., 1986. "Cartel Enforcement with Uncertainty About Costs," Working Papers 619, California Institute of Technology, Division of the Humanities and Social Sciences.
    2. Esther Hauk & Sjaak Hurkens, 1996. "Secret information acquisition in Cournot markets," Economics Working Papers 233, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 1997.
    3. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, vol. 34(1), pages 71-94, October.
    4. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
    5. Vives, Xavier, 1988. "Aggregation of Information in Large Cournot Markets," Econometrica, Econometric Society, vol. 56(4), pages 851-76, July.
    6. Lagerlöf, Johan N.M., 2003. "Insisting on a Non-negative Price: Oligopoly, Uncertainty, Welfare and Multiple Equilibria," CEPR Discussion Papers 3901, C.E.P.R. Discussion Papers.
    7. Shapiro, Carl, 1986. "Exchange of Cost Information in Oligopoly," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 433-46, July.
    8. Gal-Or, Esther, 1986. "Information Transmission-Cournot and Bertrand Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 85-92, January.
    9. Sjaak Hurkens & Nir Vulkan, 1996. "Information acquisition and entry," Economics Working Papers 155, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Li, Lode & McKelvey, Richard D. & Page, Talbot, 1987. "Optimal research for cournot oligopolists," Journal of Economic Theory, Elsevier, vol. 42(1), pages 140-166, June.
    11. Malueg, David A & Tsutsui, Shunichi O, 1998. "Oligopoly Information Exchange When Non-negative Price and Output Constraints May Bind," Australian Economic Papers, Wiley Blackwell, vol. 37(4), pages 363-71, December.
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