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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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    1. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    2. Koji Okuguchi, 1970. "Adaptive Expectations in an Oligopoly Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 233-237.
    3. Thorlund-Petersen, Lars, 1990. "Iterative computation of cournot equilibrium," Games and Economic Behavior, Elsevier, vol. 2(1), pages 61-75, March.
    4. Nabih Agiza, Hamdy & Italo Bischi, Gian & Kopel, Michael, 1999. "Multistability in a dynamic Cournot game with three oligopolists," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 51(1), pages 63-90.
    5. Seade, Jesus, 1980. "The stability of cournot revisited," Journal of Economic Theory, Elsevier, vol. 23(1), pages 15-27, August.
    6. Steffen Huck & Hans-Theo Normann & Jörg Oechssler, 2002. "Stability of the Cournot process - experimental evidence," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 123-136.
    7. al-Nowaihi, A. & Levine, P. L., 1985. "The stability of the cournot oligopoly model: A reassessment," Journal of Economic Theory, Elsevier, vol. 35(2), pages 307-321, August.
    8. Corchon, Luis C. & Mas-Colell, Andreu, 1996. "On the stability of best reply and gradient systems with applications to imperfectly competitive models," Economics Letters, Elsevier, vol. 51(1), pages 59-65, April.
    9. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    10. Bischi, Gian Italo & Naimzada, Ahmad K. & Sbragia, Lucia, 2007. "Oligopoly games with Local Monopolistic Approximation," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 371-388, March.
    11. Szidarovsky, Ferenc & Rassenti, Stephen & Yen, Jerome, 1994. "The stability of the cournot solution under adaptive expectation: A further generalization," International Review of Economics & Finance, Elsevier, vol. 3(2), pages 173-181.
    12. Luis Corchón & Andreu Mas-Colell, 1995. "A Note On Stability Of Best Reply And Gradient Systems With Applications To Imperfectly Competitive Models," Working Papers. Serie AD 1995-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    13. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    14. Rassenti, Stephen & Reynolds, Stanley S. & Smith, Vernon L. & Szidarovszky, Ferenc, 2000. "Adaptation and convergence of behavior in repeated experimental Cournot games," Journal of Economic Behavior & Organization, Elsevier, vol. 41(2), pages 117-146, February.
    15. Peng Fei & Philippe Wanner & Stephane Cotter, 1997. "Approche dynamique de la différence d'espérance de vie entre hommes et femmes en Suisse, entre 1910/11 et 1988/93. Une application des méthodes de décomposition de POLLARD et D'ARRIAGA," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 133(IV), pages 741-754, December.
    16. Cox, James C. & Walker, Mark, 1998. "Learning to play Cournot duopoly strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 36(2), pages 141-161, August.
    17. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
    18. Furth, Dave, 2009. "Anything goes with heterogeneous, but not always with homogeneous oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 183-203, January.
    19. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
    20. Franklin M. Fisher, 1961. "The Stability of the Cournot Oligopoly Solution: The Effects of Speeds of Adjustment and Increasing Marginal Costs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 125-135.
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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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