IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-04575563.html
   My bibliography  Save this paper

More memory under evolutionary learning may lead to chaos

Author

Listed:
  • Cees Diks

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

  • Cars Hommes

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

  • Paolo Zeppini

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

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Holmes, James M. & Manning, Richard, 1988. "Memory and market stability : The case of the cobweb," Economics Letters, Elsevier, vol. 28(1), pages 1-7.
    4. Honkapohja, Seppo & Mitra, Kaushik, 2003. "Learning with bounded memory in stochastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1437-1457, June.
    5. 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 322-347, April.
    6. 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.
    7. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    8. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    9. Hommes, Cars & Kiseleva, Tatiana & Kuznetsov, Yuri & Verbic, Miroslav, 2012. "Is More Memory In Evolutionary Selection (De)Stabilizing?," Macroeconomic Dynamics, Cambridge University Press, vol. 16(3), pages 335-357, June.
    10. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    11. 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.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Peiyuan Zhu & Carl Chiarella & Tony He, 2003. "Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers," Computing in Economics and Finance 2003 31, Society for Computational Economics.
    3. Hommes, Cars & Kiseleva, Tatiana & Kuznetsov, Yuri & Verbic, Miroslav, 2012. "Is More Memory In Evolutionary Selection (De)Stabilizing?," Macroeconomic Dynamics, Cambridge University Press, vol. 16(3), pages 335-357, June.
    4. Chiarella, Carl & He, Xue-Zhong & Hung, Hing & Zhu, Peiyuan, 2006. "An analysis of the cobweb model with boundedly rational heterogeneous producers," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 750-768, December.
    5. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner & Wang, Tongya, 2016. "Itchy feet vs cool heads: Flow of funds in an agent-based financial market," Journal of Economic Dynamics and Control, Elsevier, vol. 63(C), pages 53-68.
    6. Hommes, Cars H., 1998. "On the consistency of backward-looking expectations: The case of the cobweb," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 333-362, January.
    7. repec:zbw:bofrdp:2007_032 is not listed on IDEAS
    8. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    9. Yamamoto, Ryuichi, 2019. "Dynamic Predictor Selection And Order Splitting In A Limit Order Market," Macroeconomic Dynamics, Cambridge University Press, vol. 23(5), pages 1757-1792, July.
    10. Lasselle, Laurence & Svizzero, Serge & Tisdell, Clem, 2005. "Stability And Cycles In A Cobweb Model With Heterogeneous Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 9(5), pages 630-650, November.
    11. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, January.
    12. Amilon, Henrik, 2008. "Estimation of an adaptive stock market model with heterogeneous agents," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 342-362, March.
    13. F. Cavalli & A. Naimzada & M. Pireddu, 2017. "An evolutive financial market model with animal spirits: imitation and endogenous beliefs," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1007-1040, November.
    14. Hommes, Cars & van Eekelen, Arno, 1996. "Partial equilibrium analysis in a noisy chaotic market," Economics Letters, Elsevier, vol. 53(3), pages 275-282, December.
    15. Robert Kruszewski, 2013. "The Demand-Supply Model with Expectations. Complex Economic Dynamic," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 32, pages 131-141.
    16. He, Xue-Zhong & Li, Kai, 2015. "Profitability of time series momentum," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 140-157.
    17. Gian Italo Bischi & Fabio Lamantia & Davide Radi, 2018. "Evolutionary oligopoly games with heterogeneous adaptive players," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 12, pages 343-370, Edward Elgar Publishing.
    18. Raquel Almeida Ramos & Federico Bassi & Dany Lang, 2020. "Bet against the trend and cash in profits," CEPN Working Papers halshs-02956879, HAL.
    19. Federico Bassi & Raquel Ramos & Dany Lang, 2023. "Bet against the trend and cash in profits: An agent-based model of endogenous fluctuations of exchange rates," Journal of Evolutionary Economics, Springer, vol. 33(2), pages 429-472, April.
    20. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2006. "Markets do not select for a liquidity preference as behavior towards risk," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 279-292, February.
    21. Dziubiński, Marcin & Roy, Jaideep, 2012. "Popularity of reinforcement-based and belief-based learning models: An evolutionary approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 433-454.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-04575563. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.