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Describing the Dynamics and Complexity of Matsumoto‐Nonaka′s Duopoly Model

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  • Jose S. Cánovas
  • María Muñoz Guillermo

Abstract

We study the duopoly model proposed by Matsumoto and Nonaka (2006), in which two firms produce two complementary goods, and there are externalities of different signs. We analyze the topological complexity of the model by computing its topological entropy with prescribed accuracy, and, in addition, we show when such topological complexity is physically observable by characterizing the attractors. Finally, we exploit the fact that reaction maps have negative Schwarzian derivative to show the existence of absolutely continuous (with respect to Lebesgue measure) ergodic measures, and, as an economic application, we compute the average profit for almost all initial conditions.

Suggested Citation

  • Jose S. Cánovas & María Muñoz Guillermo, 2013. "Describing the Dynamics and Complexity of Matsumoto‐Nonaka′s Duopoly Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:747868
    DOI: 10.1155/2013/747868
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    References listed on IDEAS

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    1. Matsumoto, Akio & Nonaka, Yasuo, 2006. "Statistical dynamics in a chaotic Cournot model with complementary goods," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 769-783, December.
    2. 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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