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On the stability of the Cournot equilibrium: An evolutionary approach

Author

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  • Hommes, C.H.

    (University of Amsterdam)

  • Ochea, M.

    (University of Amsterdam)

  • Tuinstra, J.

    (University of Amsterdam)

Abstract

We construct an evolutionary version of Theocharis (1960)'s seminal work on the stability of equilibrium in multi-player quantity-setting oligopolies. Two sets of behavioral heuristics are investigated under fixed and endogenously evolving fractions: (myopic) Cournot firms vs. Nash firms and Cournot firms vs. rational firms. The analysis with evolutionary competition between these heuristics nests the famous Theocharis instability threshold, n=3, as a special case and shows that Theocharis' result is quite robust. For evolutionary competition between the Cournot and the rational heuristic, both the existence and the magnitude of this threshold depend on the information costs associated with the rational heuristic. When information costs are positive a bifurcation route to chaos occurs as the number of firms increases. The evolutionary model therefore exhibits perpetual but bounded fluctuations, a feature not present in Theocharis' original model.

Suggested Citation

  • Hommes, C.H. & Ochea, M. & Tuinstra, J., 2011. "On the stability of the Cournot equilibrium: An evolutionary approach," CeNDEF Working Papers 11-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    • Handle: RePEc:ams:ndfwpp:11-10
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    References listed on IDEAS

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    Cited by:

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    2. Jialu Li & Meiying Yang & Wei Xing & Xuan Zhao, 2018. "Information Acquisition Behavior: An Evolutionary Game Theory Perspective," Dynamic Games and Applications, Springer, vol. 8(2), pages 434-455, June.
    3. Domenico De Giovanni & Fabio Lamantia, 2017. "Evolutionary dynamics of a duopoly game with strategic delegation and isoelastic demand," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 877-903, November.
    4. Kopel, Michael & Lamantia, Fabio & Szidarovszky, Ferenc, 2014. "Evolutionary competition in a mixed market with socially concerned firms," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 394-409.
    5. 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.
    6. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2015. "Heterogeneity and the (de)stabilizing role of rationality," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 226-244.
    7. Cerboni Baiardi, Lorenzo & Lamantia, Fabio & Radi, Davide, 2015. "Evolutionary competition between boundedly rational behavioral rules in oligopoly games," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 204-225.
    8. Lamantia, F. & Negriu, A. & Tuinstra, J., 2016. "Evolutionary Cournot competition with endogenous technology choice: (in)stability and optimal policy," CeNDEF Working Papers 16-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    9. Gian Italo Bischi & Fabio Lamantia & Davide Radi, 2018. "Evolutionary oligopoly games with heterogeneous adaptive players," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 12, pages 343-370, Edward Elgar Publishing.
    10. Domenico De Giovanni & Fabio Lamantia, 2016. "Control delegation, information and beliefs in evolutionary oligopolies," Journal of Evolutionary Economics, Springer, vol. 26(5), pages 1089-1116, December.

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