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Walrasian versus Cournot behavior in an oligopoly of boundedly rational firms

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  • Davide Radi

    (LIUC - Università Cattaneo)

Abstract

An evolutionary oligopoly game, where firms can select between the best-reply rule and the Walrasian rule, is considered. The industry is characterized by a finite number of ex-ante homogeneous firms that, characterized by naïve expectations, decide next-period output by employing one of the two behavioral rules. The inverse demand function is linear and all firms have the same quadratic and convex cost function (decreasing return to scale). Based upon realized profits, the distribution of behavioral rules is updated according to a replicator dynamics. The model is characterized by two equilibria: the Cournot-Nash equilibrium, where all firms adopt the best-reply rule and produce the Cournot-Nash quantity, and the Walrasian equilibrium, where all firms adopt the Walrasian rule and produce the Walrasian quantity. The analysis reveals that the Walrasian equilibrium is globally stable as long as the rate of change of marginal cost exceeds the sum of residual market price sensitivities to output. If not, the Walrasian equilibrium loses stability and an attractor, representing complicated dynamics with evolutionary stable heterogeneity, arises through a bifurcation. As the propensity of firms to select the more profitable behavioral rule increases, the attractor disappears through a global bifurcation and the Cournot-Nash equilibrium can become a global Milnor attractor. To sum up, the best-reply rule can be evolutionary dominant over the Walrasian rule and this can lead an oligopoly to select the Cournot-Nash equilibrium.

Suggested Citation

  • Davide Radi, 2017. "Walrasian versus Cournot behavior in an oligopoly of boundedly rational firms," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 933-961, November.
  • Handle: RePEc:spr:joevec:v:27:y:2017:i:5:d:10.1007_s00191-017-0536-2
    DOI: 10.1007/s00191-017-0536-2
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    References listed on IDEAS

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    Cited by:

    1. Kshitija Taywade & Brent Harrison & Judy Goldsmith, 2022. "Using Non-Stationary Bandits for Learning in Repeated Cournot Games with Non-Stationary Demand," Papers 2201.00486, arXiv.org.
    2. Junyi Xu, 2021. "Reinforcement Learning in a Cournot Oligopoly Model," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1001-1024, December.
    3. 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.
    4. 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.
    5. Anufriev, Mikhail & Kopányi, Dávid, 2018. "Oligopoly game: Price makers meet price takers," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 84-103.
    6. 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.
    7. 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.
    8. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    9. Gerasimos T. Soldatos, 2021. "A model of market competition as a prize contest or a model of strife for market domination," SN Business & Economics, Springer, vol. 1(1), pages 1-9, January.
    10. Fabio Lamantia & Anghel Negriu & Jan Tuinstra, 2018. "Technology choice in an evolutionary oligopoly game," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 335-356, November.
    11. 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.
    12. Kshitija Taywade & Brent Harrison & Adib Bagh, 2022. "Modelling Cournot Games as Multi-agent Multi-armed Bandits," Papers 2201.01182, arXiv.org.
    13. Gian Italo Bischi & Fabio Lamantia, 2022. "Evolutionary oligopoly games with cooperative and aggressive behaviors," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 3-27, January.

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