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Learning Cycles in Bertrand Competition with Differentiated Commodities and Competing Learning Rules

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  • Anufriev, M.

    (University of Technology, Sydney)

  • Tuinstra, J.

    (University of Amsterdam)

  • Kopányi, D.

    (University of Amsterdam)

Abstract

This paper stresses the importance of heterogeneity in learning rules. We introduce an evolutionary competition between different learning rules and demonstrate that, though these rules can coexist, their convergence properties are strongly affected by heterogeneity. We consider a Bertrand oligopoly with differentiated goods. Firms do not have full information about the demand structure and they want to maximize their perceived one-period profit by applying one of two different learning rules: OLS learning and gradient learning. We analytically show that the stability of gradient learning depends on the distribution of learning rules over firms. In particular, as the number of gradient learners increases, gradient learning may become unstable. We study evolutionary competition between the learning rules by means of computer simulations and illustrate that this change in stability for gradient learning may lead to cyclical switching between the rules. Stable gradient learning typically gives higher average profit than OLS learning, making firms switch to gradient learning. This however, destabilizes gradient learning which, because of decreasing profits, makes firms switch back to OLS learning. This cycle may repeat itself indefinitely.

Suggested Citation

  • Anufriev, M. & Tuinstra, J. & Kopányi, D., 2012. "Learning Cycles in Bertrand Competition with Differentiated Commodities and Competing Learning Rules," CeNDEF Working Papers 12-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:12-05
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    Cited by:

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    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Sarah Mignot & Fabio Tramontana & Frank Westerhoff, 2024. "Complex dynamics in a nonlinear duopoly model with heuristic expectation formation and learning behavior," Annals of Operations Research, Springer, vol. 337(3), pages 809-834, June.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

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    More about this item

    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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