Finite size effect in EZ model

The finite size effect in the Eguiluz-Zimmermann (EZ) model is studied. It is found that the finite size effect is very impor-tant if the number of the agents N is large enough and the probability of trading among the agents is small enough: a≪1/N. In this case, the model becomes almost a big single cluster system that includes almost all the agents. For the small clusters, the size distribution can still satisfy a power law. However, the exponent will change due to the fluctuation effect. For a≫1/N, it can be proved that the fluctuation effect is not important, hence the mean field theory is correct.