Does eductive stability imply evolutionary stability?
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 twoâ€“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.
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- Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005.
"Evolutionary dynamics in markets with many trader types,"
Journal of Mathematical Economics,
Elsevier, vol. 41(1-2), pages 7-42, February.
- Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2002. "Evolutionary dynamics in markets with many trader types," CeNDEF Working Papers 02-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- 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.
- Diks, C.G.H. & Weide, R. van der, 2003. "Herding, A-synchronous Updating and Heterogeneity in Memory in a CBS," CeNDEF Working Papers 03-06, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Brock, W.A. & Hommes, C.H., 1996.
"A Rational Route to Randomness,"
9530r, Wisconsin Madison - Social Systems.
- R. Guesnerie, 2002.
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Econometric Society, vol. 70(2), pages 439-480, March.
- Guesnerie, R., 1999. "Anchoring Economic Predictions in Common Knowledge," DELTA Working Papers 1999-06, DELTA (Ecole normale supérieure).
- 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.
- Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
- Guesnerie, Roger, 1992.
"An Exploration of the Eductive Justifications of the Rational-Expectations Hypothesis,"
American Economic Review,
American Economic Association, vol. 82(5), pages 1254-78, December.
- Guesnerie, R., 1989. "An Exploration of the Eductive Justifications of the Rational Expectations Hypotbesis," DELTA Working Papers 89-24, DELTA (Ecole normale supérieure).
- 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.
- Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
- 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.
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