Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v33y2009i6p1201-1216.html
   My bibliography  Save this article

Chaos in the cobweb model with a new learning dynamic

Author

Listed:
  • Waters, George A.
Abstract
The new learning dynamic of Brown et al. [(1950). Solutions of games by differential equation. In: Kuhn, H.W., Tucker, A.W. (Eds.), Contributions to the Theory of Games I. Annals of Mathematics Studies, vol. 24. Princeton University Press, Princeton] is introduced to macroeconomic dynamics via the cobweb model with rational and naive forecasting strategies. This dynamic has appealing properties such as positive correlation and inventiveness. There is persistent heterogeneity in the forecasts and chaotic behavior with bifurcations between periodic orbits and strange attractors for the same range of parameter values as in previous studies. Unlike Brock and Hommes [(1997). A rational route to randomness. Econometrica (65), 1059-1095], however, there exist intuitively appealing steady states where one strategy dominates, and there are qualitative differences in the resulting dynamics of the two approaches. There are similar bifurcations in a parameter that represents how aggressively agents switch to better performing strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:33:y:2009:i:6:p:1201-1216
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(08)00212-1
    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. 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.
    2. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    3. William Branch & George W. Evans, 2007. "Model Uncertainty and Endogenous Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(2), pages 207-237, April.
    4. William H. Sandholm, 2009. "Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium," Games, MDPI, vol. 1(1), pages 1-15, December.
    5. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    6. 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.
    7. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution.
    8. 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.
    9. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    10. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
    11. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    12. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    13. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    14. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    15. 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.
    16. Cees Diks & Cars Hommes & Valentyn Panchenko & Roy Weide, 2008. "E&F Chaos: A User Friendly Software Package for Nonlinear Economic Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 221-244, September.
    17. Ken Binmore & Larry Samuelson, 1999. "Evolutionary Drift and Equilibrium Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 363-393.
    18. 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.
    19. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift And Equilibrium Selection," ELSE working papers 049, ESRC Centre on Economics Learning and Social Evolution.
    20. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    21. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    22. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    23. 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.
    24. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    25. Eli Ben-Sasson & Adam Tauman Kalai & Ehud Kalai, 2006. "An Approach to Bounded Rationality," Discussion Papers 1439, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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. 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.
    2. Pfajfar, Damjan, 2013. "Formation of rationally heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1434-1452.
    3. Andrea Giusto, 2015. "Learning to Agree: A New Perspective on Price Drift," Economics Bulletin, AccessEcon, vol. 35(1), pages 276-282.
    4. Ahmad Naimzada & Nicolò Pecora & Fabio Tramontana, 2019. "A cobweb model with elements from prospect theory," Journal of Evolutionary Economics, Springer, vol. 29(2), pages 763-778, April.
    5. 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.
    6. Li, Yan & Wang, Lidong, 2019. "Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 116-126.
    7. George A. Waters, 2011. "Endogenous Rational Bubbles," Working Paper Series 20111003, Illinois State University, Department of Economics.

    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. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    2. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    3. 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.
    4. 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.
    5. 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.
    6. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
    7. 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.
    8. Weibull, Jörgen & Salomonsson, Marcus, 2005. "Natural selection and social preferences," SSE/EFI Working Paper Series in Economics and Finance 588, Stockholm School of Economics, revised 27 Sep 2005.
    9. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    10. 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.
    11. repec:cdl:ucsbec:6-98 is not listed on IDEAS
    12. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
    13. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    14. 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.
    15. 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.
    16. Sandholm,W.H., 2002. "Potential dynamics and stable games," Working papers 21, Wisconsin Madison - Social Systems.
    17. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    18. 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.
    19. 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.
    20. 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.
    21. 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.

    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:dyncon:v:33:y:2009:i:6:p:1201-1216. 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/jedc .

    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.