Role of Selective Interaction in Wealth Distribution

In our simplified description ‘wealth’ is money (m). A kinetic theory of gas like model of money is investigated where two agents interact (trade) selectively and exchange some amount of money between them so that sum of their money is unchanged and thus total money of all the agents remains conserved. The probability distributions of individual money (P (m) vs. m) is seen to be influenced by certain ways of selective interactions. The distributions shift away from Boltzmann-Gibbs like exponential distribution and in some cases distributions emerge with power law tails known as Pareto’s law (P (m) ∝ m). Power law is also observed in some other closely related conserved and discrete models. A discussion is provided with numerical support to have a dig into the emergence of power laws in such models. Introduction Econophysics of Wealth distributions is an active area which involves in interpreting and analysing real economic data of money, wealth or income distributions of all kinds of people pertaining to different societies and nations [4]. A number of statistical physical models can be found in the literature [1] in connection with the above. Understanding the emergence of Pareto’s law (P (m) ∝ m), now more than a century old, is one of the most important agenda. Some early attempts [5] have been made to understand the wealth distributions, especially the Pareto’s law where the index α is generally found to be in the range of 1 to 2.5 more or less universally. Some recent works [6, 7] assume economic activities to be analogous to elastic collisions to have Kinetic theory of gas like models proposed by Chakrabarti and group and later by others (We refer this class of models as ‘Chakrabarti model’.). Analogy is drawn between Money (m) and Energy (E) where temperature (T ) is average money (< m >) of any individual at ‘equilibrium’. There has been a renewed interest in the two-agent exchange model (be it of money, energy or of something else) in the new scenario. For example, a recent work deals