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Bayesian Nash Equilibrium in "Linear" Cournot Models with Private Information about Costs

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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 Barcelona Graduate School of Economics in its series Working Papers with number 674.

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    Date of creation: Nov 2012
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    Handle: RePEc:bge:wpaper:674

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    Keywords: Cournot; private information; Bayesian Nash equilibrium;

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    1. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
    2. Lode Li, 1985. "Cournot Oligopoly with Information Sharing," RAND Journal of Economics, The RAND Corporation, vol. 16(4), pages 521-536, Winter.
    3. Lagerlof, Johan N.M., 2007. "Insisting on a non-negative price: Oligopoly, uncertainty, welfare, and multiple equilibria," International Journal of Industrial Organization, Elsevier, vol. 25(4), pages 861-875, August.
    4. Xavier Vives, 1990. "Trade Association Disclosure Rules, Incentives to Share Information, and Welfare," RAND Journal of Economics, The RAND Corporation, vol. 21(3), pages 409-430, Autumn.
    5. Sjaak Hurkens & Nir Vulkan, 1996. "Information acquisition and entry," Economics Working Papers 155, Department of Economics and Business, Universitat Pompeu Fabra.
    6. 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.
    7. Vives, Xavier, 1988. "Aggregation of Information in Large Cournot Markets," Econometrica, Econometric Society, vol. 56(4), pages 851-76, July.
    8. Esther Hauk & Sjaak Hurkens, 2001. "Secret information acquisition in Cournot markets," Economic Theory, Springer, vol. 18(3), pages 661-681.
    9. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, vol. 34(1), pages 71-94, October.
    10. Alison J. Kirby, 1988. "Trade Associations as Information Exchange Mechanisms," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 138-146, Spring.
    11. Gal-Or, Esther, 1986. "Information Transmission-Cournot and Bertrand Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 85-92, January.
    12. Shapiro, Carl, 1986. "Exchange of Cost Information in Oligopoly," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 433-46, July.
    13. 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.
    14. Hwang Hae-shin, 1993. "Optimal Information Acquisition for Heterogenous Duopoly Firms," Journal of Economic Theory, Elsevier, vol. 59(2), pages 385-402, April.
    15. Richard N. Clarke, 1983. "Collusion and the Incentives for Information Sharing," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 383-394, Autumn.
    16. 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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