Kinetic Exchange Models in Economics and Sociology

Abstract

In this article, we briefly review the different aspects and applications of kinetic exchange models in economics and sociology. Our main aim is to show in what manner the kinetic exchange models for closed economic systems were inspired by the kinetic theory of gas molecules. The simple yet powerful framework of kinetic theory, first proposed in 1738, led to the successful development of statistical physics of gases towards the end of the 19th century. This framework was successfully adapted to modeling of wealth distributions in the early 2000's. In later times, it was applied to other areas like firm dynamics and opinion formation in the society, as well. We have tried to present the flavour of the several models proposed and their applications, intentionally leaving out the intricate mathematical and technical details.

Physicists' approach to studying socio-economic inequalities: Can humans be modelled as atoms?

“…For a large number of molecules (N → ∞) and a sufficient number of time steps (t → ∞), the system reaches an equilibrium (or steady-state) distribution [30]. The equilibrium distribution turns out to be the Boltzmann-Gibbs (exponential) distribution, as shown in Fig.…”

“…6). Thus, for 0 < λ < 1, the market is effectively 'interacting' [30]. The relaxation time to reach the steady state distribution is a complicated function of the saving propensity λ and the system size N 5) are best fitted by the Gamma-distribution (see [39,40]).…”

“…Most interestingly for the physicists, the KWEMs in the regime 0 < λ < 1, seem to reproduce the energy dynamics of a D-dimensional system, with the additional remarkable feature that the corresponding dimension D can assume any real value [33,30,39], and also establishes interesting links with a generalized D-dimensional kinetic theory with real spatial dimension D [52,53]. Numerical simulations suggest that at equilibrium, the system has a Gamma-distribution of order n, coinciding with the Boltzmann-Gibbs energy distribution for a D-dimensional gas with D = 2n.…”

The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains

“…Mariacristina and Giulio [11] study the influence of agent's savings on wealth distribution and find out the factors causing wealth inequality. Other discrete models on wealth distribution can be found in [12][13][14][15][16].…”