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Cánovas, Jose S.; Muñoz Guillermo, María

Describing the dynamics and complexity of Matsumoto-Nonaka’s duopoly model. (English) Zbl 1470.91153

Abstr. Appl. Anal. 2013, Article ID 747868, 18 p. (2013).
Summary: We study the duopoly model proposed by A. Matsumoto and Y. Nonaka [“Statistical dynamics in a chaotic Cournot model with complementary goods”, J. Econ. Behav. Organ. 61, No. 4, 769–783 (2006; doi:10.1016/j.jebo.2004.07.008)], 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.

Cited in 1 Document

MSC:

91B55 Economic dynamics
37B40 Topological entropy
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References:

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