Emergence of power-law in a market with mixed models

We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Paretoʹs law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A Yardsale (YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud (TF) model in which the amount to be exchanged is a fraction of loserʹs wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, i.e., there are some agents following TF model while rest follow YS model, it leads to distribution with power-law tails. Similar effect is observed when one carries out transactions for a fraction of oneʹs wealth using TF model and for the rest YS model is used. We also observe a power-law tail in wealth distribution if we allow the agents to follow either of the models with some probability.