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Chaos in the cobweb model with a new learning dynamic

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  • Waters, George A.

Abstract

The new learning dynamic of Brown et al. [(1950). Solutions of games by differential equation. In: Kuhn, H.W., Tucker, A.W. (Eds.), Contributions to the Theory of Games I. Annals of Mathematics Studies, vol. 24. Princeton University Press, Princeton] is introduced to macroeconomic dynamics via the cobweb model with rational and naive forecasting strategies. This dynamic has appealing properties such as positive correlation and inventiveness. There is persistent heterogeneity in the forecasts and chaotic behavior with bifurcations between periodic orbits and strange attractors for the same range of parameter values as in previous studies. Unlike Brock and Hommes [(1997). A rational route to randomness. Econometrica (65), 1059-1095], however, there exist intuitively appealing steady states where one strategy dominates, and there are qualitative differences in the resulting dynamics of the two approaches. There are similar bifurcations in a parameter that represents how aggressively agents switch to better performing strategies.

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  • Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.
    • Handle: RePEc:eee:dyncon:v:33:y:2009:i:6:p:1201-1216
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    1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    2. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    3. William Branch & George W. Evans, 2007. "Model Uncertainty and Endogenous Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(2), pages 207-237, April.
    4. William H. Sandholm, 2009. "Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium," Games, MDPI, Open Access Journal, vol. 1(1), pages 1-15, December.
    5. Parke, William R. & Waters, George A., 2007. "An evolutionary game theory explanation of ARCH effects," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2234-2262, July.
    6. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    7. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
    8. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    9. 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.
    10. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, January.
    11. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    12. Cees Diks & Cars Hommes & Valentyn Panchenko & Roy Weide, 2008. "E&F Chaos: A User Friendly Software Package for Nonlinear Economic Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 221-244, September.
    13. Ken Binmore & Larry Samuelson, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Oxford University Press, vol. 66(2), pages 363-393.
    14. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    15. 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.
    16. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics,in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
    17. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    18. Eli Ben-Sasson & Adam Tauman Kalai & Ehud Kalai, 2006. "An Approach to Bounded Rationality," Discussion Papers 1439, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Parke, William R. & Waters, George A., 2014. "On The Evolutionary Stability Of Rational Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 18(07), pages 1581-1606, October.
    2. Pfajfar, Damjan, 2013. "Formation of rationally heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1434-1452.
    3. Andrea Giusto, 2015. "Learning to Agree: A New Perspective on Price Drift," Economics Bulletin, AccessEcon, vol. 35(1), pages 276-282.
    4. Waters, George A., 2010. "Instability in the cobweb model under the BNN dynamic," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 230-237, March.
    5. George A. Waters, 2011. "Endogenous Rational Bubbles," Working Paper Series 20111003, Illinois State University, Department of Economics.

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    Keywords

    Chaos Cobweb model Learning BNN;

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