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Learning cycles in Bertrand competition with differentiated commodities and competing learning rules

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  • Anufriev, Mikhail
  • Kopányi, Dávid
  • Tuinstra, Jan

Abstract

This paper stresses the importance of heterogeneity in learning. We consider a Bertrand oligopoly with firms using either least squares learning or gradient learning for determining the price. We demonstrate that convergence properties of the rules are strongly affected by heterogeneity. In particular, gradient learning may become unstable as the number of gradient learners increases. Endogenous choice between the learning rules may induce cyclical switching. Stable gradient learning gives higher average profit than least squares learning, making firms switch to gradient learning. This can destabilize gradient learning which, because of decreasing profits, makes firms switch back to least squares learning.

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  • Anufriev, Mikhail & Kopányi, Dávid & Tuinstra, Jan, 2013. "Learning cycles in Bertrand competition with differentiated commodities and competing learning rules," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2562-2581.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:12:p:2562-2581
    DOI: 10.1016/j.jedc.2013.06.010
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    Cited by:

    1. Makarewicz, Tomasz, 2021. "Traders, forecasters and financial instability: A model of individual learning of anchor-and-adjustment heuristics," Journal of Economic Behavior & Organization, Elsevier, vol. 190(C), pages 626-673.
    2. Kopányi, Dávid, 2017. "The coexistence of stable equilibria under least squares learning," Journal of Economic Behavior & Organization, Elsevier, vol. 141(C), pages 277-300.
    3. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2018. "Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 822-843, December.
    4. 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.
    5. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    6. 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.
    7. Ruben Geer & Arnoud V. Boer & Christopher Bayliss & Christine S. M. Currie & Andria Ellina & Malte Esders & Alwin Haensel & Xiao Lei & Kyle D. S. Maclean & Antonio Martinez-Sykora & Asbjørn Nilsen Ris, 2019. "Dynamic pricing and learning with competition: insights from the dynamic pricing challenge at the 2017 INFORMS RM & pricing conference," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(3), pages 185-203, June.
    8. 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.
    9. David Kopanyi & Anita Kopanyi-Peuker, 2015. "Endogenous information disclosure in experimental oligopolies," Discussion Papers 2015-11, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    10. Mignot, Sarah & Tramontana, Fabio & Westerhoff, Frank H., 2023. "Complex dynamics in a nonlinear duopoly model with heuristic expectation formation and learning behavior," BERG Working Paper Series 187, Bamberg University, Bamberg Economic Research Group.
    11. Ruben van de Geer & Arnoud V. den Boer & Christopher Bayliss & Christine Currie & Andria Ellina & Malte Esders & Alwin Haensel & Xiao Lei & Kyle D. S. Maclean & Antonio Martinez-Sykora & Asbj{o}rn Nil, 2018. "Dynamic Pricing and Learning with Competition: Insights from the Dynamic Pricing Challenge at the 2017 INFORMS RM & Pricing Conference," Papers 1804.03219, arXiv.org.
    12. 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.
    13. Makarewicz, Tomasz, 2019. "Traders, forecasters and financial instability: A model of individual learning of anchor-and-adjustment heuristics," BERG Working Paper Series 141, Bamberg University, Bamberg Economic Research Group.
    14. 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.
    15. Ahmed, E. & Elsadany, A.A. & Puu, Tonu, 2015. "On Bertrand duopoly game with differentiated goods," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 169-179.
    16. Torsten J. Gerpott & Jan Berends, 2022. "Competitive pricing on online markets: a literature review," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(6), pages 596-622, December.
    17. 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.
    18. Natalya Yu. Yaroshevich, 2020. "Production differentiation in the industrial markets for mechanical engineering: Supply factors," Upravlenets, Ural State University of Economics, vol. 11(5), pages 47-57, November.
    19. 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.

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    More about this item

    Keywords

    Bertrand competition; Heterogeneous agents; Least squares learning; Gradient learning; Endogenous switching;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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