Universal Pareto laws in agent-based exchange models: debt and varying initial-money distributions

We examine by Monte-Carlo simulations the behavior of a kinetic exchange-trading model for various initial distributions of money in the system of agents. Our goal is to analyze the characteristics of the Pareto laws for the long-time money distribution, in both closed and open systems. We consider three different initial distributions for these two situations. We first briefly summarize the concepts and results of some agent-based money-exchange models. Then, via employing the Monte-Carlo computer simulations, for both types of systems we obtain the long-time money distributions for the initially homogeneous or constant, for positive random, and finally, for both positive and negative random distributions of money among the agents. We conclude that the Pareto laws and their exponents remained nearly the same in all these situations showing little sensitivity to the initial conditions imposed. Graphic abstract