Threshold-induced phase transition in kinetic exchange models

Kinetic Models of Wealth Distribution with Extreme Inequality: Numerical Study of Their Stability against Random Exchanges

In view of some recent reports on global wealth inequality, where a small number (often a handful) of people own more wealth than 50% of the world's population, we explored if kinetic exchange models of markets could ever capture features where a significant fraction of wealth can concentrate in the hands of a few as the market size N approaches infinity. One existing example of such a kinetic exchange model is the Chakraborti or Yard-Sale model; in the absence of tax redistribution, etc., all wealth ultimately condenses into the hands of a single individual (for any value of N), and the market dynamics stop. With tax redistribution, etc., steady-state dynamics are shown to have remarkable applicability in many cases in our extremely unequal world. We show that another kinetic exchange model (called the Banerjee model) has intriguing intrinsic dynamics, where only ten rich traders or agents possess about 99.98% of the total wealth in the steady state (without any tax, etc., like external manipulation) for any large N value. We will discuss the statistical features of this model using Monte Carlo simulations. We will also demonstrate that if each trader has a non-zero probability f of engaging in random exchanges, then these condensations of wealth (e.g., 100% in the hand of one agent in the Chakraborti model, or about 99.98% in the hands of ten agents in the Banerjee model) disappear in the large N limit. Moreover, due to the built-in possibility of random exchange dynamics in the earlier proposed Goswami-Sen model, where the exchange probability decreases with the inverse power of the wealth difference between trading pairs, one does not see any wealth condensation phenomena. In this paper, we explore these aspects of statistics of these intriguing models.

Kinetic exchange income distribution models with saving propensities: inequality indices and self-organized poverty level

We report the numerical results for the steady-state income or wealth distribution [Formula: see text] and the resulting inequality measures (Gini [Formula: see text] and Kolkata [Formula: see text] indices) in the kinetic exchange models of market dynamics. We study the variations of [Formula: see text] and of the indices [Formula: see text] and [Formula: see text] with the saving propensity [Formula: see text] of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest of the population (where, in the steady state, a self-organized poverty level or SOPL appears). These studies have also been made for two different kinds of saving behaviours. One, where each agent has the same value of [Formula: see text] (constant over time) and the other where [Formula: see text] for each agent can take two values (0 and 1), changing randomly over a fraction of time [Formula: see text] of choosing [Formula: see text]. We find that the inequality decreases with increasing savings ([Formula: see text]); inequality indices ([Formula: see text] and [Formula: see text]) decrease and SOPL increases with increasing [Formula: see text], indicating possible applications in economic policy making. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Development of Econophysics: A Biased Account and Perspective from Kolkata

We present here a somewhat personalized account of the emergence of econophysics as an attractive research topic in physical, as well as social, sciences. After a rather detailed storytelling about our endeavors from Kolkata, we give a brief description of the main research achievements in a simple and non-technical language. We also briefly present, in technical language, a piece of our recent research result. We conclude our paper with a brief perspective.