Kinetic modeling of wealth distribution with adaptive social behaviors

Social behaviors play a crucial role in shaping wealth distribution in societies, while wealth distribution also significantly inuences social behaviors. To model the co-evolutionary multi-dynamics of wealth distribution and social behaviors, this study presents a kinetic model of wealth distribution with adaptive social behaviors. The model is developed within a semi-discrete framework of kinetic theory for active particles, considering a complex socio-economic system in which individuals are represented as active particles characterized by a vector-valued state encompassing their wealth level and social behavioral preference — cooperation and competition. Here, competition reects self-interested behavior that resists redistribution and reinforces wealth disparities; In contrast, cooperation is interpreted not as inherent altruism but as consensus behavior: an individual's positive attitude toward redistributive policies such as taxation and welfare that transfer resources to poorer members of society. A multiscale approach is employed, accounting for both decentralized micro-micro (m-m) interactions between individuals and regulatory micro-macro (m-M) interactions between individuals and societal-scale indicators. Numerical simulations reveal that a system with only m-m interactions tends toward polarization, exhibiting “winner-take-all” dynamics that often appear in an unregulated competitive society. In contrast, the m-M interactions, interpreted as macroscopic policy or normative control that enforces consensus, steer the system toward a more stable and balanced economic structure. This work extends kinetic socio-economic models by coupling wealth and behavioral dynamics through a co-evolutionary feedback loop, providing a useful tool for analyzing the impact of policy and social design on economic inequality.