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Nonlinear Cournot and Bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations

Author

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  • Andaluz, J.
  • Elsadany, A.A.
  • Jarne, G.

Abstract

In a differentiated triopoly model with heterogeneous firms, the local stability of the Nash equilibrium under both quantity and price competition is analyzed. We find that the presence of a firm following a gradient rule based on marginal profits, and a player with adaptive expectations, determines the local stability of the Nash equilibrium, regardless the competition type, while the effects of the degree of product differentiation on the stability depend on the nature of products. Moreover, the Nash equilibrium is more stable under quantity competition than under price competition.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:132:y:2017:i:c:p:86-99
    DOI: 10.1016/j.matcom.2016.07.001
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    References listed on IDEAS

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    Cited by:

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    2. Lorenzo Cerboni Baiardi & Ahmad K. Naimzada, 2018. "An evolutionary model with best response and imitative rules," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 313-333, November.
    3. S. S. Askar & Mona F. EL-Wakeel & M. A. Alrodaini, 2018. "Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products," Complexity, Hindawi, vol. 2018, pages 1-13, February.
    4. 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).
    5. Lorenzo Cerboni Baiardi & Ahmad K. Naimzada, 2019. "An evolutionary Cournot oligopoly model with imitators and perfect foresight best responders," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 458-475, July.
    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. G. Rigatos, 2021. "Statistical Validation of Multi-Agent Financial Models Using the H-Infinity Kalman Filter," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 777-798, October.
    8. 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).
    9. Ren, Jing & Sun, Hao & Xu, Genjiu & Hou, Dongshuang, 2023. "Convergence of output dynamics in duopoly co-opetition model with incomplete information," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 209-225.
    10. Xiaoliang Li, 2021. "Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand," Papers 2112.05950, arXiv.org.
    11. Andrikopoulos, A. & Dassiou, X., 2018. "Exchange-rate exposure in a “Rule of Three” Model," Working Papers 18/02, Department of Economics, City University London.
    12. Cerboni Baiardi, Lorenzo & Naimzada, Ahmad K., 2019. "An oligopoly model with rational and imitation rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 254-278.
    13. Sameh S Askar & Abdulrahman Al-Khedhairi, 2020. "Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game," Mathematics, MDPI, vol. 8(9), pages 1-16, August.
    14. Joaquín Andaluz & Gloria Jarne, 2019. "On price stability and the nature of product differentiation," Journal of Evolutionary Economics, Springer, vol. 29(2), pages 741-762, April.
    15. 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).

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