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More memory under evolutionary learning may lead to chaos

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Author Info

  • 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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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 392 (2013)
Issue (Month): 4 ()
Pages: 808-812

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Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:808-812

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Heterogeneous agent models; Imitation; Innovation; Memory; Stability;

References

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  1. Brock, W.A., 1995. "A Rational Route to Randomness," Working papers 9530, Wisconsin Madison - Social Systems.
  2. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
  3. Hommes, C.H. & Kiseleva, T. & Kuznetsov, Y. & Verbic, M., 2009. "Is more memory in evolutionary selection (de)stabilizing?," CeNDEF Working Papers 09-07, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  4. Jovanovic, Boyan & MacDonald, Glenn M, 1994. "The Life Cycle of a Competitive Industry," Journal of Political Economy, University of Chicago Press, vol. 102(2), pages 322-47, April.
  5. LeBaron, Blake, 2001. "Evolution And Time Horizons In An Agent-Based Stock Market," Macroeconomic Dynamics, Cambridge University Press, vol. 5(02), pages 225-254, April.
  6. Kaushik Mitra & Seppo Honkapohja, 1999. "Learning with Bounded Memory in Stochastic Models," Computing in Economics and Finance 1999 221, Society for Computational Economics.
  7. Holmes, James M. & Manning, Richard, 1988. "Memory and market stability : The case of the cobweb," Economics Letters, Elsevier, vol. 28(1), pages 1-7.
  8. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
  9. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
  10. Hart, M & Jefferies, P & Johnson, N.F & Hui, P.M, 2001. "Crowd–anticrowd theory of the minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 537-544.
  11. Hommes, Cars H., 1991. "Adaptive learning and roads to chaos : The case of the cobweb," Economics Letters, Elsevier, vol. 36(2), pages 127-132, June.
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Cited by:
  1. 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.

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