An almost linear stochastic map related to the particle system models of social sciences

TL;DR

This paper introduces a stochastic map model for economic dynamics that captures income inequality and opinion formation, showing phase transitions and power law distributions, with comparisons to physical kinetic exchange models.

Contribution

It presents a new stochastic map model that reproduces key features of economic and social phenomena, including inequality and opinion dynamics, and compares it with existing physical models.

Findings

Produces positively skewed income and wealth distributions

Exhibits non-trivial phase transitions in opinion formation

Aligns with empirical data and physical models

Abstract

We propose a stochastic map model of economic dynamics. In the last decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of income and wealth. Another area of inquiry is the formation of opinion in a society. The proposed model attempts to produce positively skewed distributions and the power law distributions as has been observed in the real data of income and wealth. Also, it shows a non-trivial phase transition in the opinion of a society (opinion formation). A number of physical models also generates similar results. In particular, the kinetic exchange models have been especially successful in this regard. Therefore, we compare the results obtained from these two approaches and discuss a number of new features and drawbacks of this model.