Application of the Deffuant Model in Money Exchange - Li, Hsin-Lun (Communications in Mathematics and Applications, 2025)
A money transfer system involves interactions between buyers and sellers, where a buyer purchases goods or services from a seller. The amount of money lost by the buyer is exactly equal to the amount gained by the seller. Over time, these transactions accumulate, influencing the overall distribution of wealth within the system. At each time step, a randomly chosen pair of socially connected agents interacts through a financial transaction, following predefined exchange rules. We extend the Deffuant opinion dynamics model to formulate a money exchange system, where interactions between agents determine the redistribution of wealth. Through this framework, we investigate the conditions under which asymptotic stability emerges, ensuring that the system reaches a steady state. Additionally, we explore whether and when an equal wealth distribution can be achieved under different interaction dynamics. By incorporating elements of social connectivity and iterative financial exchanges, our study provides insights into how simple micro-level interactions can lead to macroscopic patterns of wealth distribution. The findings contribute to the broader understanding of economic dynamics, wealth inequality, and social influence on financial transactions. This study bridges the gap between opinion dynamics and wealth exchange models, offering a novel perspective on financial stability in social systems.