  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.
