Describing the Dynamics and Complexity of Matsumoto-Nonaka's Duopoly Model | Zendy

José S. Cánovas | Zendy; María Muñoz Guillermo | Zendy

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Describing the Dynamics and Complexity of Matsumoto-Nonaka's Duopoly Model

Author(s) -

José S. Cánovas,

María Muñoz Guillermo

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/747868

Subject(s) - duopoly , mathematics , topological entropy , lebesgue measure , schwarzian derivative , ergodic theory , attractor , entropy (arrow of time) , measure (data warehouse) , absolute continuity , observable , pure mathematics , mathematical economics , lebesgue integration , computer science , mathematical analysis , physics , database , cournot competition , quantum mechanics

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

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