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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.

Suggested Citation

  • 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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    Cited by:

    1. Parke, William R. & Waters, George A., 2014. "On The Evolutionary Stability Of Rational Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 18(7), 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. Ahmad Naimzada & Nicolò Pecora & Fabio Tramontana, 2019. "A cobweb model with elements from prospect theory," Journal of Evolutionary Economics, Springer, vol. 29(2), pages 763-778, April.
    5. 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.
    6. Li, Yan & Wang, Lidong, 2019. "Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 116-126.
    7. George A. Waters, 2011. "Endogenous Rational Bubbles," Working Paper Series 20111003, Illinois State University, Department of Economics.

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    Chaos Cobweb model Learning BNN;

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