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Bertrand under Uncertainty: Private and Common Costs

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  • Johan N. M. Lagerlöf

    (Department of Economics, University of Copenhagen)

Abstract

This paper proposes an n-firm homogeneous-good Bertrand model with private information about costs. The model allows for any non-negative correlation between the cost draws and for any demand elasticity but still yields a closed-form solution. The solution is simple, in pure strategies, and involves price dispersion. For some parameter values, a weak version of the winner’s curse arises. This framework is used to study the question whether cost uncertainty softens competition. Earlier literature has shown that the answer (perhaps counter-intuitively) is “no,” while assuming (i) independent cost draws and (ii) no drastic innovations. The analysis here shows that relaxing (ii) but not (i) does not alter that result. However, when the cost draws are sufficiently highly correlated and the price elasticity of demand is sufficiently low, cost uncertainty indeed softens competition.

Suggested Citation

  • Johan N. M. Lagerlöf, 2016. "Bertrand under Uncertainty: Private and Common Costs," Discussion Papers 16-02, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:1602
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    References listed on IDEAS

    as
    1. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
    2. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    3. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
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    5. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    6. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
    7. Arozamena, Leandro & Weinschelbaum, Federico, 2009. "Simultaneous vs. sequential price competition with incomplete information," Economics Letters, Elsevier, vol. 104(1), pages 23-26, July.
    8. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Bertrand competition; Hansen-Spulber model; private information; information sharing; common values; private values; winner’s curse;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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