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Collective Sensitivity, Collective Accessibility, and Collective Kato’s Chaos in Duopoly Games

Author

Listed:
  • Hongqing Wang

    (School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China)

  • Tianxiu Lu

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Risong Li

    (School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China)

  • Yuanlin Chen

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
    South Sichuan Applied Mathematics Research Center, Zigong 643000, China)

  • Yongjiang Li

    (School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China)

  • Weizhen Quan

    (Department of Mathematics, Zhanjiang Preschool Education College, Zhanjiang 524037, China)

Abstract

By using the uniform continuity of two onto maps, this paper further explores stronger forms of Kato’s chaos, sensitivity, and accessibility of Cournot maps. In particular, the sensitivity, the collective sensitivity, the accessibility, and the collective accessibility of the compositions of two reaction functions are studied. It is observed that a Cournot onto map H on a product space is sensitive (collectively sensitive, collectively accessible, accessible, or collectively Kato chaotic) if and only if the restriction of the map H 2 to the MPE-set is sensitive as well. Several examples are given to show the necessity of the reaction functions being continuous onto maps.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4226-:d:970600
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    References listed on IDEAS

    as
    1. Yu Zhao & Risong Li, 2019. "Chaos in Duopoly Games via Furstenberg Family Couple," Complexity, Hindawi, vol. 2019, pages 1-8, November.
    2. Risong Li & Tianxiu Lu, 2020. "The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets," Complexity, Hindawi, vol. 2020, pages 1-12, September.
    3. Oprocha, Piotr & Wilczyński, Paweł, 2007. "Shift spaces and distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 347-355.
    4. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
    5. 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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