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Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty

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  • Lepore, Jason J.

Abstract

We provide new results for two-stage games in which firms make capacity investments when demand is uncertain, then, when demand is realized, compete in prices. We consider games with demand rationing schemes ranging from efficient to proportional rationing. In all cases, there is a subgame perfect equilibrium outcome coinciding with the outcome of the Cournot game with demand uncertainty if and only if (i) the fluctuation in absolute market size is small relative to the cost of capacity, or (ii) uncertainty is such that with high probability the market demand is very large and with the remaining probability the market demand is extremely small. Otherwise, equilibria involve mixed strategies. Further, we show under efficient rationing that condition (i) is sufficient for the unique equilibrium outcome to be an equilibrium outcome of the Cournot game with demand uncertainty.

Suggested Citation

  • Lepore, Jason J., 2012. "Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 177-186.
  • Handle: RePEc:eee:mateco:v:48:y:2012:i:3:p:177-186
    DOI: 10.1016/j.jmateco.2012.04.001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Attila Tasnádi, 2016. "Endogenous timing of moves in Bertrand–Edgeworth triopolies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 317-334, December.
    2. Barna Bakó & Attila Tasnádi, 2017. "The Kreps-Scheinkman Game in Mixed Duopolies," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 173(4), pages 753-768, December.
    3. Kim, Jeong-Yoo & Lee, Myeong Ho & Berg, Nathan, 2016. "Peak-load pricing in duopoly," Economic Modelling, Elsevier, vol. 57(C), pages 47-54.
    4. Robert Somogyi, 2013. "Bertrand-Edgeworth competition with substantial product differentiation," IEHAS Discussion Papers 1332, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    5. Leoni, Patrick L., 2013. "Survival in Cournot games," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 429-434.
    6. Christiaan Behrens & Mark Lijesen, 2012. "Capacity Choice under Uncertainty with Product Differentiation," Tinbergen Institute Discussion Papers 12-113/VIII, Tinbergen Institute, revised 20 Feb 2014.
    7. Tasnádi, Attila & Bakó, Barna, 2014. "A Kreps-Scheinkman-állítás érvényessége lineáris keresletű vegyes duopóliumok esetén
      [The Kreps and Scheinkman result remains valid for mixed duopolies with linear demand]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(5), pages 533-543.
    8. Jacobs, Martin, 2016. "Number of firms, rationing, matching, and knowledge: A comprehensive study of variations in experimental Kreps-Scheinkman markets," Economics Working Papers 2016-02, Christian-Albrechts-University of Kiel, Department of Economics.
    9. Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.

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