The Rich Are Different ! Pareto Law from asymmetric interactions in asset exchange models

It is known that asset exchange models with symmetric interaction between agents show either a Gibbs/log-normal distribution of assets among the agents or condensation of the entire wealth in the hands of a single agent, depending upon the rules of exchange. Here we explore the effects of introducing asymmetry in the interaction between agents with different amounts of wealth (i.e., the rich behave differently from the poor). This can be implemented in several ways: e.g., (1) in the net amount of wealth that is transferred from one agent to another during an exchange interaction, or (2) the probability of gaining vs. losing a net amount of wealth from an exchange interaction. We propose that, in general, the introduction of asymmetry leads to Pareto-like power law distribution of wealth.