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REPLICATOR DYNAMIC LEARNING IN MUTH'S MODEL OF PRICE MOVEMENTS

Published online by Cambridge University Press:  13 September 2012

Eran A. Guse  and
Joel Carton
Eran A. Guse*
Affiliation:
West Virginia University
Joel Carton
Affiliation:
Florida International University
*
Address correspondence to: Eran A. Guse, Department of Economics, College of Business and Economics, West Virginia University, Morgantown, WV 26506-6025, USA; e-mail: [email protected].
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Abstract

We investigate the stability properties of Muth's model of price movements when agents choose a production level using replicator dynamic learning. It turns out that when there is a discrete set of possible production levels, possible stable states and stability conditions differ between adaptive learning and replicator dynamic learning.

Keywords

Asymptotic stabilityReplicator dynamicsCobweb modelE-stabilityNash equilibria
Type
Articles
Information
Macroeconomic Dynamics , Volume 18 , Issue 3 , April 2014 , pp. 573 - 592
Copyright
Copyright © Cambridge University Press 2012 

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References

REFERENCES

Arifovic, Jasmina (1994) Genetic algorithm learning and the cobweb model. Journal of Economic Dynamics and Control 18, 3–28.CrossRefGoogle Scholar
Boyce, W.E. and DiPrima, R.C. (1992) Elementary Differential Equations. New York: Wiley.Google Scholar
Branch, William and McGough, Bruce (2008) Replicator dynamics in a cobweb model with rationally heterogeneous expectations. Journal of Economic Behavior and Organization 65, 224–244.CrossRefGoogle Scholar
Bray, Margaret and Savin, Nathan E. (1986) Rational expectations equilibria, learning, and model specification. Econometrica 54, 1129–1160.CrossRefGoogle Scholar
Brock, William and Hommes, Cars (1998) Heterogeneous beliefs and routes to chaos in a sample asset pricing model. Journal of Economic Dynamics and Control 22, 1235–1274.CrossRefGoogle Scholar
DeCanio, Stephen J. (1979) Rational expectations and learning from experience. Quarterly Journal of Economics 93, 47–57.CrossRefGoogle Scholar
Evans, George (1989) The fragility of sunspots and bubbles. Journal of Monetary Economics 23, 297–317.CrossRefGoogle Scholar
Evans, George and Guesnerie, Roger (1993) Rationalizability, strong rationality, and expectational stability. Games and Economic Behavior 5, 632–646.CrossRefGoogle Scholar
Evans, George and Honkapohja, Seppo (1994) Learning, convergence and stability with multiple rational expectations equilibria. European Economic Review 38, 1071–1098.CrossRefGoogle Scholar
Evans, George and Honkapohja, Seppo (1997) Least squares learning with heterogeneous expectations. Economic Letters 52, 197–201.Google Scholar
Evans, George and Honkapohja, Seppo (2001) Learning and Expectations in Macroeconomics. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Evans, George, Honkapohja, Seppo, and Marimon, Ramon (2001) Convergence in monetary inflation models with heterogeneous learning rules. Macroeconomic Dynamics 5, 1–31.CrossRefGoogle Scholar
Fourgeaud, Claude, Gourieroux, Christian, and Pradel, Jacqueline (1986) Learning procedures and convergence to rationality. Econometrica 54, 845–868.CrossRefGoogle Scholar
Fudenberg, Drew and Levine, David (1998) The Theory of Learning in Games. Cambridge, MA: MIT Press.Google Scholar
Giannitsarou, Chryssi (2003) Heterogeneous learning. Review of Economic Dynamics 6, 885–906.CrossRefGoogle Scholar
Granato, James, Guse, Eran, and Wong, M.C. Sunny (2008) Learning from the expectations of others. Macroeconomic Dynamics 12, 345–377.CrossRefGoogle Scholar
Guesnerie, Roger (1992) An exploration of the eductive justifications for the rational expectations hypothesis. American Economic Review 82, 1254–1278.Google Scholar
Guse, Eran (2005) Stability properties for learning with heterogeneous expectations and multiple equilibria. Journal of Economic Dynamics and Control 29, 1623–1642.CrossRefGoogle Scholar
Guse, Eran (2010) Heterogeneous expectations, adaptive learning, and evolutionary dynamics. Journal of Economic Behavior and Organization 74, 1623–1642.CrossRefGoogle Scholar
Honkapohja, Seppo and Mitra, Kaushik (2003) Learning with bounded memory in stochastic models. Journal of Economic Dynamics and Control 27, 1437–1457.CrossRefGoogle Scholar
Marcet, Albert and Sargent, Thomas J. (1989) Convergence of least-squares learning mechanisms in self-referential linear stochastic models. Journal of Economic Theory 48, 337–368.CrossRefGoogle Scholar
Muth, John F. (1961) Rational expectations and the theory of price movements. Econometrica 29, 315–335.CrossRefGoogle Scholar
Sethi, Rajiv and Franke, Reiner (1995) Behavioral heterogeneity under evolutionary pressure: Macroeconomic implications of costly optimisation. Economic Journal 105, 583–600.CrossRefGoogle Scholar
Taylor, Peter and Jonker, Leo (1978) Evolutionarily stable strategies and game dynamics. Mathematical Biosciences 40, 145–156.CrossRefGoogle Scholar
Weibull, Jorgen W. (1997) Evolutionary Game Theory. Cambridge, MA: MIT Press.Google Scholar