IDEAS home Printed from https://ideas.repec.org/a/hin/complx/5484629.html
   My bibliography  Save this article

Chaos in Duopoly Games via Furstenberg Family Couple

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/5484629.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/8503/2019/5484629.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2019/5484629?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Li, Risong & Wang, Hongqing & Zhao, Yu, 2016. "Kato’s chaos in duopoly games," Chaos, Solitons & Fractals, Elsevier, vol. 84(C), pages 69-72.
    3. Fabio Lamantia, 2011. "A Nonlinear Duopoly with Efficient Production-Capacity Levels," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 295-309, October.
    4. Puu, Tonu & Tramontana, Fabio, 2019. "Can Bertrand and Cournot oligopolies be combined?," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 97-107.
    5. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2018. "Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 822-843, December.
    6. Bacchiocchi, Andrea & Bischi, Gian Italo & Giombini, Germana, 2022. "Non-performing loans, expectations and banking stability: A dynamic model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Nijkamp, P. & Poot, J., 1991. "Lessons from non-linear dynamic economics," Serie Research Memoranda 0105, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    8. Xiuqin Yang & Feng Liu & Hua Wang, 2023. "Complex Dynamic Analysis for a Rent-Seeking Game with Political Competition and Policymaker Costs," Mathematics, MDPI, vol. 11(21), pages 1-18, November.
    9. Li, Wen-na & Elsadany, A.A. & Zhou, Wei & Zhu, Yan-lan, 2021. "Global Analysis, Multi-stability and Synchronization in a Competition Model of Public Enterprises with Consumer Surplus," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    10. Gangopadhyay, Partha, 2014. "Dynamics of mergers, bifurcation and chaos: A new framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 293-307.
    11. Whitby, Simon & Parker, David & Tobias, Andrew, 2001. "Non-linear dynamics and duopolistic competition: a R&D model and simulation," Journal of Business Research, Elsevier, vol. 51(3), pages 179-191, March.
    12. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    13. Roberto Cellini & Fabio Lamantia, 2015. "Quality competition in markets with regulated prices and minimum quality standards," Journal of Evolutionary Economics, Springer, vol. 25(2), pages 345-370, April.
    14. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    15. A. Matsumoto, 2006. "Controlling the Cournot-Nash Chaos," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 379-392, February.
    16. 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.
    17. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    18. Bischi Gian Italo & Lamantia Fabio, 2012. "Routes to Complexity Induced by Constraints in Cournot Oligopoly Games with Linear Reaction Functions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-30, April.
    19. Hommes, C.H. & Ochea, M. & Tuinstra, J., 2011. "On the stability of the Cournot equilibrium: An evolutionary approach," CeNDEF Working Papers 11-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    20. Yu Zhao & Waseem Anwar & Risong Li & Tianxiu Lu & Zhiwen Mo, 2023. "Distributional Chaos and Sensitivity for a Class of Cyclic Permutation Maps," Mathematics, MDPI, vol. 11(15), pages 1-9, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:5484629. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.