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Competition analysis of a triopoly game with bounded rationality

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  • Elsadany, A.A.

Abstract

A dynamic Cournot game characterized by three boundedly rational players is modeled by three nonlinear difference equations. The stability of the equilibria of the discrete dynamical system is analyzed. As some parameters of the model are varied, the stability of Nash equilibrium is lost and a complex chaotic behavior occurs. Numerical simulation results show that complex dynamics, such as, bifurcations and chaos are displayed when the value of speed of adjustment is high. The global complexity analysis can help players to take some measures and avoid the collapse of the output dynamic competition game.

Suggested Citation

  • Elsadany, A.A., 2012. "Competition analysis of a triopoly game with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1343-1348.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:11:p:1343-1348
    DOI: 10.1016/j.chaos.2012.07.003
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    References listed on IDEAS

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    1. Okuguchi, Koji & Irie, Kazuya, 1990. "The Schur and Samuelson Conditions for a Cubic Equation," The Manchester School of Economic & Social Studies, University of Manchester, vol. 58(4), pages 414-418, December.
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    4. Naimzada, Ahmad K. & Sbragia, Lucia, 2006. "Oligopoly games with nonlinear demand and cost functions: Two boundedly rational adjustment processes," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 707-722.
    5. Ma, Jun-Hai & Ji, Wei-Zhuo, 2009. "Complexity of repeated game model in electric power triopoly," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1735-1740.
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    Citations

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    Cited by:

    1. A. A. Elsadany & A. M. Awad, 2019. "Dynamics and chaos control of a duopolistic Bertrand competitions under environmental taxes," Annals of Operations Research, Springer, vol. 274(1), pages 211-240, March.
    2. Cavalli, Fausto & Naimzada, Ahmad, 2016. "Complex dynamics and multistability with increasing rationality in market games," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 151-161.
    3. Yujing Yang & Wenzhe Tang, 2018. "Research on a 3D Predator-Prey Evolutionary System in Real Estate Market," Complexity, Hindawi, vol. 2018, pages 1-13, February.
    4. Liu, Cui & He, Rui-chun & Zhou, Wei & Li, Hui, 2021. "Dynamic analysis of airline bidding game based on nonlinear cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    5. Wentao Yi & Chunqiao Tan, 2019. "Bertrand Game with Nash Bargaining Fairness Concern," Complexity, Hindawi, vol. 2019, pages 1-22, August.
    6. 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).
    7. Xin Su & Shengsen Duan & Shubing Guo & Haolong Liu, 2018. "Evolutionary Games in the Agricultural Product Quality and Safety Information System: A Multiagent Simulation Approach," Complexity, Hindawi, vol. 2018, pages 1-13, March.
    8. Xiaoliang Li, 2021. "Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand," Papers 2112.05950, arXiv.org.
    9. Junhai Ma & Weiya Di & Hao Ren, 2017. "Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service," Complexity, Hindawi, vol. 2017, pages 1-12, September.

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