Kinetic modeling of wealth distribution under individual and collective transactions with heterogeneous saving propensities

To investigate wealth distribution from both microscopic and mesoscopic perspectives, the individual, collective, and hybrid exchange models are introduced with heterogeneous saving propensities. The hybrid kinetic framework integrates collective transactions with individual exchanges that occur either within each group or across all agents. Two representative scenarios of group saving propensities are examined: bipolar and arithmetic distributions. The resulting wealth distributions are characterized through the Gini coefficient and entropy. The analysis reveals that the coexistence of collective and individual interactions amplifies wealth inequality, particularly when collective transactions are coupled with intra-group individual exchanges. Moreover, the entropy is linked to the overlap degree between the wealth distribution and the Boltzmann–Gibbs function. Detailed examinations of the Lorenz curves and probability density functions provide theoretical insight into the intriguing phenomenon that both the Gini coefficient and entropy exhibit either monotonic or non-monotonic dependencies on the saving propensity.