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On the dynamics of Kopel’s Cournot duopoly model

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  • Cánovas, J.S.
  • Muñoz-Guillermo, M.

Abstract

In this paper we study the duopoly model proposed by M. Kopel [26], where two firms compete “a la Cournot” and the reaction curves have a higher degree of coupling in the sense that firms have to make their choices simultaneously. We will make a descriptive analysis of the two-dimensional model, making an approach through particular situations. On the other hand, when the firms are homogeneous a one-dimensional invariant subset is present in the model. We will give an analytical proof of the existence of a (topological) chaotic behavior for a wide range of parameter values and we will study when chaotic synchronization and collusion occur.

Suggested Citation

  • Cánovas, J.S. & Muñoz-Guillermo, M., 2018. "On the dynamics of Kopel’s Cournot duopoly model," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 292-306.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:292-306
    DOI: 10.1016/j.amc.2018.02.043
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    References listed on IDEAS

    as
    1. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
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