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Introduction

To date, the study of cellular automata and genetic programming have proceeded largely on parallel paths. This article studies the evolution of cellular automata in which the cells each contain data and genetic programs. The immediate application of this convergence is to study how different legal rules affect the evolution of learning and behavior in an economy. Drawing on the disciplines of computer science, biology, law, and economics, the article provides a new "artificial intelligence" tool for use in economic modeling. The typical "Coase Theorem" [1] scenario, in which neighbors engage in activities that may detrimentally affect each other, is to explore some of the capabilities of the new tool [2].

The authors use the Mathematica programming language to implement their conception. They create a ring of sites, each of which contain genetic programs [3] for determining the behavior and learning strategy of that site. These genetic programs are created using a flexible template mechanism that facilitates specification of a complex grammar for permissible programs, as was demonstrated for the evolution of Lindenmayer systems and plant growth programs [4]. The rich set of primitives of these programs include sensing operations, such as determination of the behaviors of neighboring sites and mating operations that permit programs of neighboring sites to be adopted in part or in their entirety. These primitives thus permit the sites to learn from each other and, in a deeply recursive manner, to learn how the other sites themselves learn. This is a novel approach of combining evolutionary algorithms and, in particular, genetic programming techniques [5, 6, 7] with interacting agents modeled by cellular automata.

The ring of sites (the economy) evolves through a multistage iteration. First, the programs of the sites are evaluated in a cascading fashion to determine the future course of learning by the site, the immediate program for determining behavior, and the actual behavior resulting from the interaction of the behavior program with local and global features of the economy. The behaviors are in turn evaluated to determine certain global parameters (such as the prices of various commodities within the economy) and the consequences of the local interactions created as a result of the behaviors and the legal rules applicable thereto. This process permits a computation of the fitness of each of the sites within the economy. The final state of each evolutionary iteration permits the programs at each site to mutate based in part on the fitness of the site. The coevolution of these sites is modeled through the repetition of these iterations. The emphasis in this paper is on the development and validation of the tools necessary for this form of modeling and not on particular results.


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