A simple trading model based on pair pattern strategy space with holding periods is proposed. Power-law behaviors are observed for the return variance $σ^2$, the price impact $H$ and the predictability $K$ for both models with linear and square root impact functions. The sum of the traders' wealth displays a positive value for the model with square root price impact function, and a qualitative explanation is given based on the observation of the conditional excess demand $$. An evolutionary trading model is further proposed, and the elimination mechanism effectively changes the behavior of the traders highly performed in the model without evolution. The trading model with other types of traders, e.g., traders with the MG's strategies and producers, are also carefully studied.

22 pages, 16 figures