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Nonlinear dynamics in the Cournot duopoly game with heterogeneous players

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  • Agiza, H.N.
  • Elsadany, A.A.
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    Abstract

    We analyze a nonlinear discrete-time Cournot duopoly game, where players have heterogeneous expectations. Two types of players are considered: boundedly rational and naive expectations. In this study we show that the dynamics of the duopoly game with players whose beliefs are heterogeneous, may become complicated. The model gives more complex chaotic and unpredictable trajectories as a consequence of increasing the speed of adjustment of boundedly rational player. The equilibrium points and local stability of the duopoly game are investigated. As some parameters of the model are varied, the stability of the Nash equilibrium point is lost and the complex (periodic or chaotic) behavior occurs. Numerical simulations are presented to show that players with heterogeneous beliefs make the duopoly game behave chaotically. Also, we get the fractal dimension of the chaotic attractor of our map which is equivalent to the dimension of Henon map.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437102016485
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 320 (2003)
    Issue (Month): C ()
    Pages: 512-524

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    Handle: RePEc:eee:phsmap:v:320:y:2003:i:c:p:512-524

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Discrete dynamical systems; Cournot duopoly games; Complex dynamics; Heterogeneous expectations;

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    Cited by:
    1. Ahmad Naimzada & Fabio Tramontana, 2011. "Double route to chaos in an heterogeneous triopoly game," Quaderni di Dipartimento 149, University of Pavia, Department of Economics and Quantitative Methods.
    2. Luciano Fanti & Luca Gori, 2011. "Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations," Discussion Papers 2011/122, Dipartimento di Scienze Economiche (DSE), University of Pisa, Pisa, Italy.
    3. Luciano Fanti & Luca Gori, 2011. "The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited," Discussion Papers 2011/120, Dipartimento di Scienze Economiche (DSE), University of Pisa, Pisa, Italy.
    4. Fanti, Luciano & Gori, Luca, 2011. "Stability analysis in a Cournot duopoly with managerial sales delegation and bounded rationality," MPRA Paper 33828, University Library of Munich, Germany.
    5. Luciano Fanti & Luca Gori, 2011. "Stability in a Cournot duopoly under asymmetric unionism," Discussion Papers 2011/123, Dipartimento di Scienze Economiche (DSE), University of Pisa, Pisa, Italy.
    6. Luciano Fanti, 2012. "The dynamics of a banking duopoly with capital regulations," Discussion Papers 2012/151, Dipartimento di Scienze Economiche (DSE), University of Pisa, Pisa, Italy.
    7. Fanti, Luciano & Gori, Luca, 2011. "Efficient bargaining versus right to manage: a stability analysis with heterogeneous players in a duopoly with quantity competition and trade unions," MPRA Paper 34434, University Library of Munich, Germany.
    8. Tomasz Dubiel-Teleszyński, 2010. "Complex Dynamics in a Bertrand Duopoly Game with Heterogeneous Players," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 2(2), pages 95-116, March.
    9. Luciano Fanti & Luca Gori, 2011. "The dynamics of a differentiated duopoly with quantity competition," Discussion Papers 2011/121, Dipartimento di Scienze Economiche (DSE), University of Pisa, Pisa, Italy.
    10. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," MPRA Paper 37834, University Library of Munich, Germany.
    11. Fanti, Luciano & Gori, Luca, 2011. "Cross-ownership and stability in a Cournot duopoly," MPRA Paper 34574, University Library of Munich, Germany.
    12. Luciano Fanti, 2012. "Environmental standards and Cournot duopoly: a stability analysis," Discussion Papers 2012/154, Dipartimento di Scienze Economiche (DSE), University of Pisa, Pisa, Italy.
    13. repec:ebl:ecbull:v:3:y:2008:i:4:p:1-9 is not listed on IDEAS
    14. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
    15. Xin, Baogui & Chen, Tong, 2011. "On a master-slave Bertrand game model," Economic Modelling, Elsevier, vol. 28(4), pages 1864-1870, July.
    16. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.

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