Modeling altruism and selfishness in welfare dynamics: The role of nonlinear interactions

This paper deals with the modeling, qualitative and numerical analysis, of welfare dynamics in societies viewed as complex evolutive systems subject to different policies of wealth distribution. A nonlinear model of wealth distribution is presented. The state of a population is modeled by a probability distribution over wealth classes and the dynamic of interaction is parameterized by a threshold, whose dynamics depends on an internal competition related to the wealth distribution. Therefore, the model is a system of equations in which the threshold is one of the dynamic variables. The approach contains the whole path from modeling to simulations, through a qualitative analysis of the initial value problem.