Does a rising tide lift all boats? A wealth exchange model on a dynamic network with economic growth

Wealth inequality, although an age-old problem, has seen a substantial rise since the early XXI century. The distributions of wealth and income across countries follow a universal pattern, typically manifesting as a two-class division, which suggests that fundamental mechanisms underpin the emergence of these economic disparities. Agent-based models, which allow the rules of interaction between economic agents to be explicitly defined, are particularly well-suited for studying economic systems and analyzing their emergent properties. In this work, we examine a recently proposed dynamic complex network agent-based model within the context of a growing economy. The model evolves via three alternating processes: independent stochastic wealth growth of each agent, wealth exchanges between connected agents, and the rewiring of connections within the complex network. The wealth growth of each agent is governed by a stochastic process characterized by two parameters: a drift term $\mu$, representing economic growth, and volatility $\sigma$, reflecting heterogeneity in productivity. We analyze the outcomes for various values of a social protection factor $f$, which favors the poorer agent in each transaction. Higher values of $f$ amplify the effect of economic growth: while increasing $\mu$ reduces inequality, increasing $\sigma$ has the opposite effect. In this context, economic growth benefits the poorest agents only when strong social protection is in place.