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Instability in the cobweb model under the BNN dynamic

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  • Waters, George A.

Abstract

The cobweb model where firms choose between rational and naive forecasting strategies has a 2-cycle when the slope of supply is greater than the slope of demand for a number of different dynamics describing the evolution of strategy choices. This paper proves that the 2-cycle is exponentially unstable under the learning dynamic of Brown et al. (1950). Issues arising in the analysis of piecewise smooth discrete time maps are discussed.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:2:p:230-237
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    References listed on IDEAS

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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. 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.
    3. Goeree, Jacob K. & Hommes, Cars H., 2000. "Heterogeneous beliefs and the non-linear cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 761-798, June.
    4. Branch, William A. & McGough, Bruce, 2008. "Replicator dynamics in a Cobweb model with rationally heterogeneous expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 65(2), pages 224-244, February.
    5. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    6. Sethi, Rajiv & Franke, Reiner, 1995. "Behavioural Heterogeneity under Evolutionary Pressure: Macroeconomic Implications of Costly Optimisation," Economic Journal, Royal Economic Society, vol. 105(430), pages 583-600, May.
    7. 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.
    8. 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.
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    Keywords

    Chaos Cobweb model Learning BNN;

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