Wealth distribution on a dynamic complex network

Abstract

We present an agent-based model that examines the microscopic exchange of wealth in a dynamic network to investigate the topological characteristics associated with economic inequality. The model consists of two processes: conservative wealth exchange between connected agents and the rewiring of connections, which depends on the wealth of the agents. The dynamics of wealth and connections are interrelated, as the network structure influences which agents interact with each other. We analyze the time evolution and asymptotic characteristics of the model for different values of a social protection factor ($f$), which favors the poorest agent in each wealth transaction. Our results show that for $f=0$, wealth and connections condense in a single agent, in accordance with mean-field models of wealth exchange. When $f$ is low, agents from the middle and upper classes become favored, leading to the formation of network hubs. However, as $f$ increases, the restriction of the network on exchanges results in an egalitarian society departing from the outcomes observed in the mean-field exchange models.