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Jie-Shin Lin and Chris Birchenhall
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Jie-Shin Lin: University of Manchester

No 327, Computing in Economics and Finance 2000 from Society for Computational Economics

Abstract: The last years have been seen an extraordinary flourishing of works studying learning and adaptive behaviour in diverse fields. Following the fashion of computer innovation, there has been a growing interest in application to economic models of learning procedure developed in evolutionary computation tools such as genetic algorithms. Accordingly then, the use of computer simulation based on the related genetic algorithms (GAs) has largely taken by many researchers, for example, Axelord (1987), Marimon, McGrattan and Sargent (1990), Arifovic (1994, 1995a, 1995b), Arifovic and Eaton (1995), Dawid (1996a, 1996b), Birchenhall (1995), Birchenhall et al (1997), Bullard and Duffy (1997), Riechmann (1998, 1999), and Vriend (1998).We study a simple overlapping generation economy as an adaptive learning system. There are two populations co-existing in each period of time. A significant departure to representative agent in economic modelling is a release of hypothesis of perfect foresight or rational expectation. As a result, individual agents in the economy have heterogeneous beliefs concerning realisation of possible outcomes. With the existence of heterogeneity in the economy, actual outcome may or may not identical to any particular individual agent' expectation ex-ante. When the actual outcome feeds back to individual agents' beliefs, individual agents learn to correctly update their own beliefs. The learning is via a so-called genetic algorithm process.The framework proposed here is identical to the one considered in Bullard and Duffy (1998). Two prime questions raised are firstly the explanation of appearance of convergence to the Pareto superior equilibrium, and secondly how robust its convergence is to the changes in parameter value of the model, in particular, there are distinctions in two respects: within one learning scheme and between learning schemes. Moreover, we will look at what Vriend (1998) addressed a so-called "spite-effect"; in an economic setting, the effect of the economic forces might lead to significantly different results when applied computational tools between individual and social learning.We investigate performances of Holland's standard GA (SGA), Arifovic's augmented GA (AGA), and Birchenhall's selective transfer GA (STGA). Compared to modern artificial adaptive techniques, Maynard Smith's replicator model in its simple formulation highlighting the role of selection has been successfully applied in economics. In this study, the results from the replicator dynamics are compared to results of the related GAs above. In addition, we modify these learning algorithms. The results are compared to the results of their originals. Our work suggests that the stability of the Pareto superior equilibrium of the model is robust i.e. independent of the precise algorithm used. Finally, a further work for the study is necessary, even if it is a little speculative. While the learning schemes are not derived from an explicit behavioural model, one learning algorithm can be only described as a specific form of learning process. In other words, we ask which learning scheme agent will use population-wide when agent has many learning schemes available.

Date: 2000-07-05
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