This paper presents results from an experiemtal computer simulated stock market. In this market artificial intelligence algorithms take on the role of traders. They make predictions about the future, and buy and sell stock an indicated by their expectations of future risk and return.

We startd out this paper with a list of Facts that financial theorizing should attempt to explain. We discussed the Facts in enough detail so that the reader can appreciate the caution one needs to display while interpreting evidence form financial databases.

We have set out a general framework for adaptive belief systems in asset pricing thery. Fluctuations in prices and returns are driven by an evolutionary dynamics between traders with different expectations about prices.

The properties of prices, especially with respect to initial conditions related to market startup and unusual shocks to the market environment, are of concern to regulators assessing alternative financial market structures. A natural way to investigate the importance of initial conditions is to...