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Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization

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

Abstract

In this paper, we maximize the utility function under budget constraint in an oligopoly market. We consider a Cournot duopoly model with boundedly rational players adopting the gradient adjustment mechanism to update their productions. The dynamics of Cournot duopoly model with relative profit delegation maximization is analyzed. We explore the local stability of Nash equilibrium point and the occurrence of complexity behaviors. Additionally, the chaotic dynamics of this game via flip bifurcations and Neimark–Sacker bifurcations are researched. Numerical simulations are presented to show bifurcation diagrams, sensitive dependence on initial conditions, strange attractors and chaos. As to the fractal structure emerged in evolution process, the fractal dimension is calculated. Further analysis of the simulation results indicates that the chaotic behavior of the system can be stabilized on the Nash equilibrium point by using state variables feedback and parameter variation method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:560:y:2020:i:c:s0378437120306130
    DOI: 10.1016/j.physa.2020.125174
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    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. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization and equivalence of Cournot and Bertrand equilibria in asymmetric duopoly," Economics Bulletin, AccessEcon, vol. 34(2), pages 819-827.
    3. 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.
    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. Ahmed, E. & Elettreby, M.F., 2014. "Controls of the complex dynamics of a multi-market Cournot model," Economic Modelling, Elsevier, vol. 37(C), pages 251-254.
    6. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization and equivalence of Cournot and Bertrand equilibria in an asymmetric differentiated duopoly," MPRA Paper 55895, University Library of Munich, Germany.
    7. 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.
    8. Zhang, Ming & Wang, Guanghui & Xu, Jin & Qu, Cunquan, 2020. "Dynamic contest model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    9. 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).
    10. Hommes,Cars, 2015. "Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems," Cambridge Books, Cambridge University Press, number 9781107564978, October.
    11. Michael Kopel & Luca Lambertini, 2013. "On Price Competition with Market Share Delegation Contracts," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 34(1), pages 40-43, January.
    12. 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.
    13. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1469-1478.
    14. 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.
    15. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2015. "Nonlinear dynamics in a Cournot duopoly with isoelastic demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 129-143.
    16. Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2014. "Local and global dynamics in a duopoly with price competition and market share delegation," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 253-270.
    17. Gori, Luca & Sodini, Mauro & Fanti, Luciano, 2015. "A nonlinear Cournot duopoly with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 178-190.
    18. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization in asymmetric oligopoly: Cournot and Bertrand equilibria," MPRA Paper 55883, University Library of Munich, Germany.
    19. Atsuhiro SATOH & Yasuhito TANAKA, 2016. "Equivalence of Cournot and Bertrand equilibria in duopoly under relative profit maximization: A general analysis," Journal of Economics and Political Economy, KSP Journals, vol. 3(3), pages 513-523, September.
    20. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    21. 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.
    22. 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.
    23. 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.
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    Cited by:

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    6. Guennady Ougolnitsky & Alexey Korolev, 2023. "Game-Theoretic Models of Coopetition in Cournot Oligopoly," Stats, MDPI, vol. 6(2), pages 1-20, May.

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