Introduction

Rational expectations can be the result of a dynamic adaptive process by learning agents during which systematic mistakes in expectations are eliminated. The theory of rational expectations relies on this observation to defend its strict assumptions concerning the expectation formation of agents. However, the concrete design of the adaptation and selection processes, whether they exist and produce the „desired“ rational behaviour, is in general not considered. The common econometric instruments are not adjusted to this problem. The process should satisfy some optimality claims like the convergence speed, a feedback between result and expectation. Otherwise it is not convincing that all agents use the same learning scheme.

While the modelling of the dynamics by Bayesian learning or ordinaryleast- squares (OLS) estimators has attracted attentions since the 70’s, only in 1993 Sargent takes a new approach by creating artificial „bounded rational“ agents. He claims and provides evidence that the results of rational expectations models are unchanged if the (fully) rational agent is replaced by a learning agent whose process of expectation adaptation is generated by evolutionary algorithms or other tools of artificial intelligence like neuronal nets. Further work in which results of the mainstream theory could be reproduced by simulations with evolutionary algorithms seem to support Sargent’s hypothesis5.

In this paper I investigate the use of a genetic algorithm as a simulation tool of bounded rational asset traders in a Grossman-Stiglitz environment. A genetic algorithm is a biologically inspired stochastic parallel optimizing technique, which manipulates a generation of individuals in order to produce a new, better adapted generation. The algorithm first being developed by Holland on the basis of his observations of natural systems can be seen as an extreme simplification of the principle of evolution, i.e. the survival of the fittest.

The application to the asset market model is as follows: a population of heterogeneous market participants is simulated. The explicit optimizing behaviour of the agents is replaced by a stochastic trial-and-error process. For that purpose the operators of the genetic algorithm represent imitation of successful behaviour (selection), communication between traders (crossover) and experimentation or committing errors (mutation). Depending on their market success the trader adapts the forecast or keeps it. The process of expectation formation is simulated for different parameter settings and is compared to the rational expectations values and reference scenarios with Ordinary-Least-Square-Learning. Simulations with genetic algorithm forecasts show similar results compared to OLS-estimators in certain data constellation. The forecasts of the traders tend to the theoretical results of an equilibrium with rational expectations for a broad set of parameters. This succeeds although the traders are modelled with less computational capability and less information than in the OLS-scenarios.