UvA - DARE ( Digital Academic Repository ) 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 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. Acknowledgements: We would like to thank Buz Brock for stimulating discussions, and Roger Guesnerie and an anonymous referee for helpful comments and suggestions on an earlier draft. Remaining imperfections are of our own making. Financial support from the Netherlands Organization for Scientific Research (NWO) by a NWOMaGW Pionier grant, a NWO-MaGW VIDI grant and by the EU 7 framework collaborative project “Monetary, Fiscal and Structural Policies with Heterogeneous Agents (POLHIA)”, grant no. 225408, is gratefully acknowledged. Corresponding author: Cars Hommes, Center for Nonlinear Dynamics in Economics and Finance (CeNDEF), Department of Quantitative Economics, University of Amsterdam, Roetersstraat 11, NL-1018 WB Amsterdam, The Netherlands, e-mail: [email protected]