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Nonlinear dynamics in a Cournot duopoly with isoelastic demand

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  • Fanti, Luciano
  • Gori, Luca
  • Sodini, Mauro

Abstract

This paper analyses the dynamics of a nonlinear Cournot duopoly with general isoelastic demand (quasi-linear preferences) and quantity-setting firms that have incomplete information about the market demand. Unlike existing papers, we propose a model where the price elasticity of demand is different from one. This causes interesting local and global dynamic events that cannot be observed in the case of unit-elastic demand and homogeneous players. In particular, the global behaviour of the map is studied through the critical curves technique, and numerical simulations show coexistence of attractors, coordination failures and complex structures of the basins of attraction.

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  • 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.
    • Handle: RePEc:eee:matcom:v:108:y:2015:i:c:p:129-143
    DOI: 10.1016/j.matcom.2013.09.004
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    Cited by:

    1. Luca Gori & Nicolò Pecora & Mauro Sodini, 2017. "Market share delegation in a nonlinear duopoly with quantity competition: the role of dynamic entry barriers," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 905-931, November.
    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. Ueda, Masahiko, 2019. "Effect of information asymmetry in Cournot duopoly game with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Cerboni Baiardi, Lorenzo & Naimzada, Ahmad K., 2018. "An oligopoly model with best response and imitation rules," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 193-205.
    5. 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.
    6. Luca Gori & Luca Guerrini & Mauro Sodini, 2014. "Hopf Bifurcation in a Cobweb Model with Discrete Time Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, June.
    7. 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.
    8. Gori, Luca & Sodini, Mauro, 2017. "Price competition in a nonlinear differentiated duopoly," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 557-567.
    9. Liu, Yuxia & Zhou, Wei & Wang, Qian, 2022. "Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    10. Sun, Yanru & Sun, Hao & Sun, Panfei & Jin, Xuanzhu, 2024. "A dynamic surge pricing model throughout product lifecycle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 139-151.
    11. Cavalli, Fausto & Naimzada, Ahmad, 2015. "Effect of price elasticity of demand in monopolies with gradient adjustment," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 47-55.
    12. 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.
    13. Andrea Caravaggio & Lorenzo Cerboni Baiardi & Mauro Sodini, 2021. "A note on symmetry breaking in a non linear marketing model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 507-531, December.
    14. Zhu, Yan-lan & Zhou, Wei & Chu, Tong, 2022. "Analysis of complex dynamical behavior in a mixed duopoly model with heterogeneous goods," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    15. 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.
    16. 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.
    17. Brianzoni, Serena & Campisi, Giovanni & Colasante, Annarita, 2022. "Nonlinear banking duopoly model with capital regulation: The case of Italy," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    18. 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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    More about this item

    Keywords

    Cournot; Isoelastic demand; Nonlinear dynamics;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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