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Does eductive stability imply evolutionary stability?

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  • Hommes, C.H.
  • Wagener, F.O.O.

    () (Universiteit van Amsterdam)

Abstract

This note presents a simple example of a model in which the unique rational expectations (RE) steady state equilibrium is eductively stable in the sense of Guesnerie (2002), but where evolutionary learning, as introduced in Brock and Hommes (1997), does not necessarily converge to the RE steady state price. The example is a Muthian cobweb model where producers have heterogeneous expectations and select forecasting strategies based upon recent realized profits. By means of a simple three types example we show that a locally stable RE fundamental steady state may co-exists with a locally stable two--cycle. We also study the Muthian model with a large number of different producer types, and investigate conditions under which an evolutionary adaptive learning process based upon recent realized profits enforces global convergence to the stable RE steady state and when persistent periodic price fluctuations can arise.

Suggested Citation

  • Hommes, C.H. & Wagener, F.O.O., 2003. "Does eductive stability imply evolutionary stability?," CeNDEF Working Papers 03-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:03-04
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    References listed on IDEAS

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    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. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    3. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    4. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, pages 7-42.
    5. Diks, Cees & van der Weide, Roy, 2005. "Herding, a-synchronous updating and heterogeneity in memory in a CBS," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 741-763, April.
    6. Anufriev, M. & Assenza, T. & Hommes, C.H. & Massaro, D., 2008. "Interest Rate Rules with Heterogeneous Expectations," CeNDEF Working Papers 08-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    7. Hommes, C.H. & Wagener, F.O.O., 2008. "Complex evolutionary systems in behavioral finance," CeNDEF Working Papers 08-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    8. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March.
    9. Guesnerie, Roger, 1992. "An Exploration of the Eductive Justifications of the Rational-Expectations Hypothesis," American Economic Review, American Economic Association, vol. 82(5), pages 1254-1278, December.
    10. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
    11. Diks, Cees & van der Weide, Roy, 2005. "Herding, a-synchronous updating and heterogeneity in memory in a CBS," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 741-763, April.
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    Cited by:

    1. George W. Evans & Roger Guesnerie & Bruce McGough, 2010. "Eductive Stability in Real Business Cycle Models," University of Oregon Economics Department Working Papers 2010-16, University of Oregon Economics Department.
    2. Hommes, Cars, 2011. "The heterogeneous expectations hypothesis: Some evidence from the lab," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 1-24, January.
    3. repec:hal:journl:halshs-00975002 is not listed on IDEAS
    4. Desgranges, Gabriel & Gauthier, Stéphane, 2016. "Rationalizability and efficiency in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 163-176.
    5. Anufriev, M. & Assenza, T. & Hommes, C.H. & Massaro, D., 2008. "Interest Rate Rules with Heterogeneous Expectations," CeNDEF Working Papers 08-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    6. Gerunov, Anton, 2014. "Критичен Преглед На Основните Подходи За Моделиране На Икономическите Очаквания
      [A Critical Review of Major Approaches for Modeling Economic Expectations]
      ," MPRA Paper 68797, University Library of Munich, Germany.
    7. Pecora, Nicolò & Spelta, Alessandro, 2017. "Managing monetary policy in a New Keynesian model with many beliefs types," Economics Letters, Elsevier, vol. 150(C), pages 53-58.
    8. Bao, Te & Duffy, John, 2016. "Adaptive versus eductive learning: Theory and evidence," European Economic Review, Elsevier, vol. 83(C), pages 64-89.
    9. Nicolò Pecora & Alessandro Spelta, 2013. "Macroeconomic Stability and Heterogeneous Expectations," DEM Working Papers Series 037, University of Pavia, Department of Economics and Management.

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