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




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

  • Mikhail Anufriev & D?½vid Kop?½nyiz & Jan Tuinstra, 2013. "Learning Cycles in Bertrand Competition with Differentiated Commodities and Competing Learning Rules," Working Paper Series 8, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
  • Handle: RePEc:uts:ecowps:8

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    References listed on IDEAS

    1. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    2. Gal-Or, Esther, 1985. "First Mover and Second Mover Advantages," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 649-653, October.
    3. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    4. 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.
    5. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    6. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
    7. Mikhail Anufriev & Cars Hommes, 2012. "Evolutionary Selection of Individual Expectations and Aggregate Outcomes in Asset Pricing Experiments," American Economic Journal: Microeconomics, American Economic Association, vol. 4(4), pages 35-64, November.
    8. Bonanno, Giacomo & Christopher Zeeman, E., 1985. "Limited knowledge of demand and oligopoly equilibria," Journal of Economic Theory, Elsevier, vol. 35(2), pages 276-283, August.
    9. Theo Offerman & Jan Potters & Joep Sonnemans, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 973-997.
    10. 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.
    11. Anufriev, M. & Tuinstra, J. & Bao, T., 2013. "Fund Choice Behavior and Estimation of Switching Models: An Experiment," CeNDEF Working Papers 13-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    12. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, January.
    13. Bonanno, Giacomo, 1988. "Oligopoly Equilibria When Firms Have Local Knowledge of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 45-55, February.
    14. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, January.
    15. Ido Erev & Eyal Ert & Alvin E. Roth, 2010. "A Choice Prediction Competition for Market Entry Games: An Introduction," Games, MDPI, Open Access Journal, vol. 1(2), pages 1-20, May.
    16. Furth, Dave, 1986. "Stability and instability in oligopoly," Journal of Economic Theory, Elsevier, vol. 40(2), pages 197-228, December.
    17. Gates, D J & Rickard, J A & Wilson, D J, 1977. "A Convergent Adjustment Process for Firms in Competition," Econometrica, Econometric Society, vol. 45(6), pages 1349-1363, September.
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    Cited by:

    1. Kopányi, Dávid, 2017. "The coexistence of stable equilibria under least squares learning," Journal of Economic Behavior & Organization, Elsevier, vol. 141(C), pages 277-300.
    2. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2016. "Evolutionary Competition between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," THEMA Working Papers 2016-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. 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.
    4. repec:eee:apmaco:v:251:y:2015:i:c:p:169-179 is not listed on IDEAS
    5. repec:spr:joevec:v:27:y:2017:i:5:d:10.1007_s00191-017-0536-2 is not listed on IDEAS
    6. 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.

    More about this item


    Bertrand competition; heterogeneous agents; least squares learning; gradient learning; endogenous switching; learning cycle;

    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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