Study on Evolvement Complexity in an Artificial Stock Market
  An artificial stock market is established based on multi-agent . Each agent has a limit memory of the history of stock price, and will choose an action according to his memory and trading strategy. The trading strategy of each agent evolves ceaselessly as a result of self-teaching mechanism. 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 L\'{e}vy 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. 
Chun-Xia Yang, Tao Zhou, Pei-Ling Zhou, Jun Liu and Zi-Nan Tang