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On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility

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  • Pierre von Mouche
  • Federico Quartieri

Abstract

We consider a class of homogeneous Cournot oligopolies with concave integrated price flexibility and convex cost functions. We provide new results about the semi-uniqueness and uniqueness of (Cournot) equilibria for the oligopolies that satisfy these conditions. The condition of concave integrated price flexibility is implied by (but does not imply) the log-concavity of a continuous decreasing price function. So, our results generalize previous results for decreasing log-concave price functions and convex cost functions. We also discuss the particular type of quasi-concavity that characterizes the conditional revenue and profit functions of the firms in these oligopolies and we point out an error of the literature on the equilibrium uniqueness in oligopolies with log-concave price functions. Finally, we explain how the condition of concave integrated price flexibility relates to other conditions on the price and aggregate revenue functions usually considered in the literature, e.g., their concavity. Copyright The Author(s) 2013

Suggested Citation

  • Pierre von Mouche & Federico Quartieri, 2013. "On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility," Journal of Global Optimization, Springer, vol. 57(3), pages 707-718, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:707-718
    DOI: 10.1007/s10898-012-9926-z
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    References listed on IDEAS

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    1. Christian Ewerhart, 2009. "Cournot Oligopoly and Concavo-Concave Demand," IEW - Working Papers 427, Institute for Empirical Research in Economics - University of Zurich.
    2. Amir, R., 1996. "Cournot oligopoly and theory of supermodular games," LIDAM Reprints CORE 1228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    4. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
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    Cited by:

    1. Pierre von Mouche & Federico Quartieri, 2015. "Cournot Equilibrium Uniqueness in Case of Concave Industry Revenue: a Simple Proof," Economics Bulletin, AccessEcon, vol. 35(2), pages 1299-1305.

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