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

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  • Sjaak Hurkens

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.

Suggested Citation

  • Sjaak Hurkens, 2012. "Bayesian Nash Equilibrium in "Linear" Cournot Models with Private Information about Costs," Working Papers 674, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:674
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    References listed on IDEAS

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    Cited by:

    1. Michel Mougeot & Florence Naegelen, 2007. "Was Chadwick right?," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 30(2), pages 121-137, March.

    More about this item

    Keywords

    cournot; private information; Bayesian Nash equilibrium;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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