Kinetic modelling of economic markets with individual and collective transactions

TL;DR

This paper introduces two kinetic exchange models to analyze how individual and collective transactions influence wealth distribution and inequality in closed economic markets, revealing the contrasting effects of transaction types and saving behaviors.

Contribution

It develops dual-layered kinetic models incorporating collective and individual transactions with saving propensities, highlighting their impact on wealth inequality and market dynamics.

Findings

Collective transactions increase wealth inequality within groups.

Individual transactions across groups reduce inequality and promote wealth redistribution.

Saving propensities and collective transaction thresholds significantly affect market deviation and entropy.

Abstract

Two kinetic exchange models are proposed to explore the dynamics of closed economic markets characterized by random exchanges, saving propensities, and collective transactions. Model I simulates a system where individual transactions occur among agents with saving tendencies, along with collective transactions between groups. Model II restricts individual transactions to agents within the same group, but allows for collective transactions between groups. A three-step trading process--comprising intergroup transactions, intragroup redistribution, and individual exchanges--is developed to capture the dual-layered market dynamics. The saving propensity is incorporated using the Chakraborti-Chakrabarti model, applied to both individual and collective transactions. Results reveal that collective transactions increase wealth inequality by concentrating wealth within groups, as indicated by higher Gini coefficients and Kolkata indices. In contrast, individual transactions across groups mitigate inequality through more uniform wealth redistribution. The interplay between saving propensities and collective transactions governs deviation degree and entropy, which display inverse trends. Higher saving propensities lead to deviations from the Boltzmann-Gibbs equilibrium, whereas specific thresholds result in collective transaction dominance, producing notable peaks or troughs in these metrics. These findings underscore the critical influence of dual-layered market interactions on wealth distribution and economic dynamics.