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More memory under evolutionary learning may lead to chaos

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  • Diks, Cees
  • Hommes, Cars
  • Zeppini, Paolo

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.

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  • Diks, Cees & Hommes, Cars & Zeppini, Paolo, 2013. "More memory under evolutionary learning may lead to chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 808-812.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:808-812
    DOI: 10.1016/j.physa.2012.10.045
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    References listed on IDEAS

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    Cited by:

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    8. 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.
    9. 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.
    10. 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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