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Chaos in Duopoly Games via Furstenberg Family Couple

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  • Yu Zhao
  • Risong Li

Abstract

Assume that and are two given closed subintervals of and that and are continuous maps. Let be a Cournot map over the space . In this paper, we study - chaos (resp. strong - chaos) of such a Cournot map. We will show that the following are true: (1) is - chaotic (resp. strong - chaotic) if and only if is - chaotic (resp. strong - chaotic) if and only if is - chaotic (resp. strong - chaotic). (2) is - chaotic (resp. strong - chaotic) if and only if is - chaotic (resp. strong - chaotic). (3) is - chaotic (resp. strong - chaotic) if and only if so is . MR(2000) Subject Classification : Primary 37D45, 54H20, and 37B40 and Secondary 26A18 and 28D20.

Suggested Citation

  • Yu Zhao & Risong Li, 2019. "Chaos in Duopoly Games via Furstenberg Family Couple," Complexity, Hindawi, vol. 2019, pages 1-8, November.
    • Handle: RePEc:hin:complx:5484629
    DOI: 10.1155/2019/5484629
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    References listed on IDEAS

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    1. Oprocha, Piotr & Wilczyński, Paweł, 2007. "Shift spaces and distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 347-355.
    2. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
    3. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
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    Cited by:

    1. Hongqing Wang & Tianxiu Lu & Risong Li & Yuanlin Chen & Yongjiang Li & Weizhen Quan, 2022. "Collective Sensitivity, Collective Accessibility, and Collective Kato’s Chaos in Duopoly Games," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

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