IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v373y2020ics0096300319310197.html
   My bibliography  Save this article

Dynamics of Hotelling triopoly model with bounded rationality

Author

Listed:
  • Peng, Yu
  • Lu, Qian
  • Wu, Xue
  • Zhao, Yueru
  • Xiao, Yue

Abstract

It is devoted to introduce and research a triopoly Hotelling model with a triangular market in this paper. Based on bounded rationality, a three-dimensional discrete dynamical system is formulated. The complex dynamics which occur in the process of chaotic evolution have been investigated. The solution of Nash equilibrium gives rise to complicated phenomena as some parameters of the model are varied. Some numerical simulations are used to portray such chaotic behavior. Furthermore, proper control scheme is applied to keep the system from instability and chaos, which is also supported by some simulations.

Suggested Citation

  • Peng, Yu & Lu, Qian & Wu, Xue & Zhao, Yueru & Xiao, Yue, 2020. "Dynamics of Hotelling triopoly model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    • Handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319310197
    DOI: 10.1016/j.amc.2019.125027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319310197
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.125027?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Elsadany, A.A., 2012. "Competition analysis of a triopoly game with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1343-1348.
    3. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
    4. Agliari, A. & Naimzada, A.K. & Pecora, N., 2016. "Nonlinear dynamics of a Cournot duopoly game with differentiated products," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 1-15.
    5. Jyh‐Fa Tsai & Fu‐Chuan Lai, 2005. "Spatial duopoly with triangular markets," Papers in Regional Science, Wiley Blackwell, vol. 84(1), pages 47-59, March.
    6. Andaluz, J. & Elsadany, A.A. & Jarne, G., 2017. "Nonlinear Cournot and Bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 86-99.
    7. Xiao, Yue & Peng, Yu & Lu, Qian & Wu, Xue, 2018. "Chaotic dynamics in nonlinear duopoly Stackelberg game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1980-1987.
    8. Kleer, Robin & Piller, Frank T., 2019. "Local manufacturing and structural shifts in competition: Market dynamics of additive manufacturing," International Journal of Production Economics, Elsevier, vol. 216(C), pages 23-34.
    9. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    10. Peng, Yu & Lu, Qian, 2015. "Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 259-268.
    11. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    12. Orlov, Anton, 2016. "Effects of higher domestic gas prices in Russia on the European gas market: A game theoretical Hotelling model," Applied Energy, Elsevier, vol. 164(C), pages 188-199.
    13. Peng, Yu & Wang, Bing-Hong & Zeng, Qing-Ke & Lu, Qian & Wang, Hong, 2012. "The use of a data envelopment analysis efficient rule to produce a steady and high cooperation frequency in a spatial evolvement game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2000-2006.
    14. Agiza, H.N. & Hegazi, A.S. & Elsadany, A.A., 2002. "Complex dynamics and synchronization of a duopoly game with bounded rationality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 133-146.
    15. Ding, Zhanwen & Li, Qiang & Jiang, Shumin & Wang, Xuedi, 2015. "Dynamics in a Cournot investment game with heterogeneous players," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 939-950.
    16. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
    17. Ahmed, E. & Elsadany, A.A. & Puu, Tonu, 2015. "On Bertrand duopoly game with differentiated goods," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 169-179.
    18. Peng, Yu & Lu, Qian & Xiao, Yue, 2016. "A dynamic Stackelberg duopoly model with different strategies," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 128-134.
    19. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.
    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. Zhao, Dan & Wang, Jian & Li, Ye-kai & Tang, Jin-huan & Zhang, Shui-wang, 2024. "How to promote the transition of fuel vehicle enterprises under dual credit policy? An improved tripartite evolutionary game analysis with time delay," Energy, Elsevier, vol. 293(C).
    2. Yu, Hui & Li, Ying & Wang, Wei, 2023. "Optimal innovation strategies of automakers with market competition under the dual-credit policy," Energy, Elsevier, vol. 283(C).
    3. Xi, Xuan & Zhang, Yulin, 2021. "Complexity analysis of production, fertilizer-saving level, and emission reduction efforts decisions in a two-parallel agricultural product supply chain," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Li Cheng & Liu Conglin, 2023. "Game analysis and pricing strategy of duopoly airlines based on service," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(3), pages 1103-1124, June.
    5. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

    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. Peng, Yu & Lu, Qian & Xiao, Yue & Wu, Xue, 2019. "Complex dynamics analysis for a remanufacturing duopoly model with nonlinear cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 658-670.
    2. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    3. Yang, Xuenan & Peng, Yu & Xiao, Yue & Wu, Xue, 2019. "Nonlinear dynamics of a duopoly Stackelberg game with marginal costs," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 185-191.
    4. Zhou, Jie & Zhou, Wei & Chu, Tong & Chang, Ying-xiang & Huang, Meng-jia, 2019. "Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R&D spillover and product differentiation," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 358-378.
    5. S. S. Askar, 2020. "Duopolistic Stackelberg game: investigation of complex dynamics and chaos control," Operational Research, Springer, vol. 20(3), pages 1685-1699, September.
    6. Tian, Yi & Ma, Junhai & Xie, Lei & Koivumäki, Timo & Seppänen, Veikko, 2020. "Coordination and control of multi-channel supply chain driven by consumers’ channel preference and sales effort," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    7. Yu Yu & Weisheng Yu, 2019. "The Complexion of Multi-period Stackelberg Triopoly Game with Bounded Rationality," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 457-478, January.
    8. 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).
    9. Askar, S.S. & Al-khedhairi, A., 2020. "On complex dynamic investigations of a piecewise smooth nonlinear duopoly game," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Yan, Bo & Ahmadi, Atefeh & Mehrabbeik, Mahtab & Rajagopal, Karthikeyan & He, Shaobo & Jafari, Sajad, 2022. "Expanding the duopoly Stackelberg game with marginal costs into a multipoly game with lowering the burden of mathematical calculations: a numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. Zhang, Ming & Wang, Guanghui & Xu, Jin & Qu, Cunquan, 2020. "Dynamic contest model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    12. Peng, Yu & Lu, Qian & Xiao, Yue, 2016. "A dynamic Stackelberg duopoly model with different strategies," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 128-134.
    13. Garmani, Hamid & Ait Omar, Driss & El Amrani, Mohamed & Baslam, Mohamed & Jourhmane, Mostafa, 2020. "Analysis of a dynamics duopoly game with two content providers," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    14. Pierre Picard & Takatoshi Tabuchi, 2010. "Self-organized agglomerations and transport costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 565-589, March.
    15. S. S. Askar & A. Al-khedhairi, 2019. "Analysis of a Four-Firm Competition Based on a Generalized Bounded Rationality and Different Mechanisms," Complexity, Hindawi, vol. 2019, pages 1-12, May.
    16. Gillian Hadfield & Eric Talley, "undated". "On Public versus Private Provision of Corporate Law," American Law & Economics Association Annual Meetings 1063, American Law & Economics Association.
    17. Xiaoliang Li & Bo Li, 2023. "A Bertrand duopoly game with differentiated products reconsidered," Papers 2301.01007, arXiv.org.
    18. Ralph Braid, 2014. "The socially optimal and equilibrium locations of two stores or libraries with consumer search," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 123-136, August.
    19. Heijnen, Pim & Soetevent, Adriaan R., 2018. "Price competition on graphs," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 161-179.
    20. Sameh S. Askar, 2020. "The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game," Mathematics, MDPI, vol. 8(7), pages 1-12, July.

    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:eee:apmaco:v:373:y:2020:i:c:s0096300319310197. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.