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The techniques and code outlined in this article can be put to many uses. The samples below illustrate how these techniques have been used to examine a standard problem in the economic analysis of law. Hitherto, this problem has generally been studied using only conventional techniques based on the dubious assumptions of complete rationality and optimization. We have used our work to study the evolution of behavior and learning in an "economy" in which the costs of the activities of the agents are sometimes externalized onto neighboring agents. We find that, under certain circumstances, including certain rules of law, the behavior of the agents coevolves to resemble closely that which an external authority might impose in order to maximize wealth. A fuller understanding of these experiments can be found in the notebooks listed under Additional Materials, available through The Mathematica Journal web site. We hope that the samples below will stimulate an appetite for further examination of these notebooks and for further explorations in this field.

A Graphic Showing the Evolution of Behaviors in an Economy

In the image below, the darker areas represent farming. The lighter areas represent ranching. As in Figure 2 above, each row represents the economy at one point in time. Time moves forward as one moves down the image.

A Graphics Array Showing Market Prices in an Evolving Economy

This graphic illustrates how the prices of the two products generated by the sample economy (vegetables and cows) move together as the agents evolve their behaviors.

A Graphic Showing Profits in an Evolving Economy

This graphic illustrates how the total wealth of the economy varies as the agents evolve their behaviors.

A Table Showing Behavior Programs of Agents in an Economy After Co-Evolution

This table gives the behavior programs of the agents in an economy after coevolving under certain rules of law. These programs are generated through the process described in this article.

A Table Showing How Agents in an Economy Evolve to Learn How to Learn

A feature of our experiment was to let the agents evolve their own rules for learning and, indeed, for learning how to learn. The table below provides an example of these meta-programs that coevolve in our economy.

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