IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v46y2010i2p230-237.html
   My bibliography  Save this article

Instability in the cobweb model under the BNN dynamic

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(09)00137-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tesfatsion, Leigh & Judd, Kenneth L., 2006. "Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics," Staff General Research Papers Archive 10368, Iowa State University, Department of Economics.
    2. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    3. 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.
    4. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Parke, William R. & Waters, George A., 2014. "On The Evolutionary Stability Of Rational Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 18(7), pages 1581-1606, October.
    3. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    4. 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.
    5. Witte, Björn-Christopher, 2011. "Removing systematic patterns in returns in a financial market model by artificially intelligent traders," BERG Working Paper Series 82, Bamberg University, Bamberg Economic Research Group.
    6. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    7. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    8. Deniz Erdemlioglu & Nikola Gradojevic, 2021. "Heterogeneous investment horizons, risk regimes, and realized jumps," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 617-643, January.
    9. Serena Brianzoni & Roy Cerqueti & Elisabetta Michetti, 2010. "A Dynamic Stochastic Model of Asset Pricing with Heterogeneous Beliefs," Computational Economics, Springer;Society for Computational Economics, vol. 35(2), pages 165-188, February.
    10. 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.
    11. Yamamoto, Ryuichi & Hirata, Hideaki, 2013. "Strategy switching in the Japanese stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 2010-2022.
    12. Pascal Seppecher & Isabelle Salle & Dany Lang, 2019. "Is the market really a good teacher?," Journal of Evolutionary Economics, Springer, vol. 29(1), pages 299-335, March.
    13. Daniele Giachini, 2018. "Rationality and Asset Prices under Belief Heterogeneity," LEM Papers Series 2018/07, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    14. He, Xue-Zhong & Li, Youwei, 2015. "Testing of a market fraction model and power-law behaviour in the DAX 30," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 1-17.
    15. Frijns, Bart & Lehnert, Thorsten & Zwinkels, Remco C.J., 2010. "Behavioral heterogeneity in the option market," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2273-2287, November.
    16. 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.
    17. Gaffeo, Edoardo & Molinari, Massimo, 2017. "Taxing financial transactions in fundamentally heterogeneous markets," Economic Modelling, Elsevier, vol. 64(C), pages 322-333.
    18. Anufriev, Mikhail & Panchenko, Valentyn, 2009. "Asset prices, traders' behavior and market design," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1073-1090, May.
    19. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    20. 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.

    More about this item

    Keywords

    Chaos Cobweb model Learning BNN;

    Statistics

    Access and download statistics

    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:eee:mateco:v:46:y:2010:i:2:p:230-237. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.