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More memory under evolutionary learning may lead to chaos

Author

Listed:
  • Cees Diks

    (CeNDEF - Center for Nonlinear Dynamics in Economics and Finance - UvA - Universiteit van Amsterdam = University of Amsterdam)

  • Cars Hommes

    (CeNDEF - Center for Nonlinear Dynamics in Economics and Finance - UvA - Universiteit van Amsterdam = University of Amsterdam)

  • Paolo Zeppini

    (CeNDEF - Center for Nonlinear Dynamics in Economics and Finance - UvA - Universiteit van Amsterdam = University of Amsterdam, TU/e - Eindhoven University of Technology [Eindhoven])

Abstract

We show that an increase of memory of past strategy performance in a simple agent-based innovation model, with agents switching between costly innovation and cheap imitation, can be quantitatively stabilising while at the same time qualitatively destabilising. As memory in the fitness measure increases, the amplitude of price fluctuations decreases, but at the same time a bifurcation route to chaos may arise. The core mechanism leading to the chaotic behaviour in this model with strategy switching is that the map obtained for the system with memory is a convex combination of an increasing linear function and a decreasing non-linear function.

Suggested Citation

  • Cees Diks & Cars Hommes & Paolo Zeppini, 2013. "More memory under evolutionary learning may lead to chaos," Post-Print hal-04575563, HAL.
    • Handle: RePEc:hal:journl:hal-04575563
    DOI: 10.1016/j.physa.2012.10.045
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    2. Agliari, Anna & Naimzada, Ahmad & Pecora, Nicolò, 2017. "Dynamic effects of memory in a cobweb model with competing technologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 340-350.
    3. He, Kaijian & Lu, Xingjing & Zou, Yingchao & Keung Lai, Kin, 2015. "Forecasting metal prices with a curvelet based multiscale methodology," Resources Policy, Elsevier, vol. 45(C), pages 144-150.
    4. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    5. Tapia Cortez, Carlos A. & Hitch, Michael & Sammut, Claude & Coulton, Jeff & Shishko, Robert & Saydam, Serkan, 2018. "Determining the embedding parameters governing long-term dynamics of copper prices," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 186-197.
    6. Xu, Liang & Cao, Xianbin & Du, Wenbo & Li, Yumeng, 2018. "Effects of taxation on the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 63-68.
    7. He, Kaijian & Xu, Yang & Zou, Yingchao & Tang, Ling, 2015. "Electricity price forecasts using a Curvelet denoising based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 1-9.
    8. Fabio Lamantia & Anghel Negriu & Jan Tuinstra, 2018. "Technology choice in an evolutionary oligopoly game," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 335-356, November.
    9. Kukacka, Jiri & Barunik, Jozef, 2013. "Behavioural breaks in the heterogeneous agent model: The impact of herding, overconfidence, and market sentiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5920-5938.
    10. Cavalli, Fausto & Naimzada, Ahmad, 2015. "A tâtonnement process with fading memory, stabilization and optimal speed of convergence," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 116-129.
    11. Lamantia, F. & Negriu, A. & Tuinstra, J., 2016. "Evolutionary Cournot competition with endogenous technology choice: (in)stability and optimal policy," CeNDEF Working Papers 16-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

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