Adaptive Learning And Multiple Equilibria

Interaction among autonomous decision-makers is usually modelled in economics in game-theoretic terms or within the framework of General Equilibrium. Game-theoretic and General Equilibrium models deal almost exclusively with the existence of equilibria and do not analyse the processes which might lead to them. Even when existence proofs can be given, two questions are still open. The first concerns the possibility of multiple equilibria, which game theory has shown to be the case even in very simple models and which makes the outcome of interaction unpredictable. The second relates to the computability and complexity of the decision procedures which agents should adopt and questions the possibility of reaching an equilibrium by means of an algorithmically implementable strategy. Some theorems have recently proved that in many economically relevant problems equilibria are not computable. A different approach to the problem of strategic interaction is a "constructivist" one. Such a perspective, instead of being based upon an axiomatic view of human behaviour grounded on the principle of optimisation, focuses on algorithmically implementable "satisfycing" decision procedures. Once the axiomatic approach has been abandoned, decision procedures cannot be deduced from rationality assumptions, but must be the evolving outcome of a process of learning and adaptation to the particular environment in which the decision must be made. This paper considers one of the most recently proposed adaptive learning models: Genetic Programming and applies it to one the mostly studied and still controversial economic interaction environment, that of oligopolistic markets. Genetic Programming evolves decision procedures, represented by elements in the space of functions, balancing the exploitation of knowledge previously obtained with the search of more productive procedures. The results obtained are consistent with the evidence from the observation of the behaviour of real economic agents.

The fact that I have the opportunity to present a second edition of this monograph is an indicator for the growing size of the community concerned with agent-based computational economics. The rapid developments in this field make it very difficult to keep a volume like this, which is partly devoted to surveying the literature, up to date. I have done my best to incorporate the relevant new developments in this revised edition but it is in the nature of such a work that the selection of material covered is biased by the authors personal interest and his informational constraints. My apologies go to all researchers in this field whose work is not or not adequately represented in this book. Besides the correction of some errors and typos several additions have been made. In the literature survey sections 2.4 (which was also reorganized) and 3.5 new material was added. I have also added a new section in chapter 3 which deals with the question how well empirically observed phenomena can be explained by GA simulations. A new section in chapter 6 presents a rather extensive analysis of the behavior of a two population GA in the framework of a sealed bid double auction market. Further minor additions and changes were made throughout the text.

It is demonstrated in this paper that adaptive learning in least squares sense may be incapable to reduce, in a satisfactory way, the number of attainable equilibria in a rational expectations model. The model investigated, as an illustration, is the monetary approach to exchange rate determination that is augmented with technical trading in the currency market in the form of moving averages since it is the most commonly used technique according to questionnaire surveys. Because of technical trading in foreign exchange, the current exchange rate is dependent on jmax lags of the exchange rate, and the model has, therefore jmax + 1 nonbubble rational expectations equilibria (REE), where most of them are adaptively learnable. However, by assuming that a solution to the model should have a solution to a nested model as its limit, it is possible to single out a unique equilibrium among the adaptively learnable equilibria that is economically meaningful.

A crucial challenge for economists is figuring out how people interpret the world and form expectations that will likely influence their economic activity. Inflation, asset prices, exchange rates, investment, and consumption are just some of the economic variables that are largely explained by expectations. Here George Evans and Seppo Honkapohja bring new explanatory power to a variety of expectation formation models by focusing on the learning factor. Whereas the rational expectations paradigm offers the prevailing method to determining expectations, it assumes very theoretical knowledge on the part of economic actors. Evans and Honkapohja contribute to a growing body of research positing that households and firms learn by making forecasts using observed data, updating their forecast rules over time in response to errors. This book is the first systematic development of the new statistical learning approach. Depending on the particular economic structure, the economy may converge to a standard rational-expectations or a "rational bubble" solution, or exhibit persistent learning dynamics. The learning approach also provides tools to assess the importance of new models with expectational indeterminacy, in which expectations are an independent cause of macroeconomic fluctuations. Moreover, learning dynamics provide a theory for the evolution of expectations and selection between alternative equilibria, with implications for business cycles, asset price volatility, and policy. This book provides an authoritative treatment of this emerging field, developing the analytical techniques in detail and using them to synthesize and extend existing research.