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.
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- 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.
- Theo Offerman & Jan Potters & Joep Sonnemans, 1997. "Imitation and Belief Learning in an Oligopoly Experiment," Tinbergen Institute Discussion Papers 97-116/1, Tinbergen Institute.
- Offerman, T.J.S. & Potters, J.J.M. & Sonnemans, J., 2002. "Imitation and belief learning in an oligopoly experiment," Other publications TiSEM a6a771c5-31ba-4193-8f76-a, Tilburg University, School of Economics and Management.
- 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.
- 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.
- 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.
- Droste, E. & Hommes, C.H. & Tuinstra, J., 1999. "Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition," CeNDEF Working Papers 99-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- 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.
- 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.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, July.
- 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.
- William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
- Brock, W.A., 1995. "A Rational Route to Randomness," Working papers 9530, Wisconsin Madison - Social Systems.
- Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
- 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.
- Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, July.
- Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
- Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
- 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.
- Anufriev, M. & Hommes, C.H., 2011. "Evolutionary Selection of Individual Expectations and Aggregate Outcomes in Asset Pricing Experiments," CeNDEF Working Papers 11-06, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- 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.
- Furth, Dave, 1986. "Stability and instability in oligopoly," Journal of Economic Theory, Elsevier, vol. 40(2), pages 197-228, December.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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