An artificial stock market is established based on the multi-agent model. Each agent has a limited memory of the history of stock price, and will choose an action according to its memory and trading strategy The trading strategy of each agent evolves ceaselessly as a result of a self-teaching mechanism. The simulation results exhibit that large events are frequent in the fluctuation of the stock price generated by the present model when compared with a normal process, and the price returns distribution is a Lévy distribution in the central part followed by an approximately exponential truncation. In addition, by defining a variable to gauge the evolvement complexity of this system, we have found a phase cross-over from simple-phase to complex-phase along with the increase of the number of individuals, which may be a ubiquitous phenomenon in multifarious real-life systems.
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