We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce (quenched) saving propensity of the agents, distributed widely between the agents (0 ≤ λ < 1). The system remarkably self-organizes to a critical Pareto distribution of money P (m) ∼ m −(ν+1) with ν ≃ 1. We analyse the robustness (universality) of the distribution in the model. We also argue that although the fractional saving ingredient is a bit unnatural one in the context of gas models, our model is the simplest so far, showing selforganized criticality, and combines two century-old distributions: Gibbs (1901) Considerable investigations have already been made to study the nature of income or wealth distributions in various economic communities, in particular, in different countries. For more than a hundred years, it is known that the probability distribution P (m) for income or wealth of the individuals in the market decreases with the wealth m following a power law, known as Pareto law [1]:where the value of the exponent ν is found to lie between 1 and 2 [2,3,4]. It is also known that typically less than 10% of the population in any country possesses about 40% of the wealth and follow the above power law. The rest of the low-income group population, in fact the majority, clearly follows a different law, identified very recently to be the Gibbs distribution [5,6,7]. Studies on real data show that the high income group indeed follow Pareto law, with ν varying from 1.6 for USA [6], to 1.8 − 2.2 in Japan [3]. The value of ν thus seem to vary a little from economy to economy. We have studied here numerically a gas model of a trading market. We have considered the effect of saving propensity of the traders. The saving propensity is assumed to have a randomness. Our observations indicate that Gibbs and Pareto distributions fall in the same category and can appear naturally in the century-old and well-established kinetic theory of gas [8]: Gibbs distribution for no saving and Pareto distribution for agents with quenched random saving propensity. Our model study also indicates the appearance of self-organized criticality [9] in the simplest model so far, namely in the kinetic theory of gas models, when the stability effect of savings [10] is incorporated.We consider an ideal-gas model of a closed economic system where total money M and total number of agents * Electronic address: arnab@cmp.saha.ernet.in N is fixed. No production or migration occurs and the only economic activity is confined to trading. Each agent i, individual or corporate, possess money m i (t) at time t. In any trading, a pair of traders i and j randomly exchange their money [5,7,11], such that their total money is (locally) conserved and none end up with negative money (m i (t) ≥ 0, i.e, debt not allowed):time (t) changes by one unit after each trading. The steady-state (t → ∞) distribution of money is Gibbs one:Hence...

The distribution of wealth and income is never uniform, and philosophers and economists have tried for years to understand the reasons and formulate remedies for such inequalities. This book introduces the elegant and intriguing kinetic exchange models that physicists have developed to tackle these issues. This is the first monograph in econophysics focused on the analyses and modelling of these distributions, and is ideal for physicists and economists. It explores the origin of economic inequality. It is written in simple, lucid language, with plenty of illustrations and in-depth analyses, making it suitable for researchers new to this field as well as more specialized readers. bikas k. chakrabarti is a Senior Professor of Theoretical Condensed Matter Physics at the Saha Institute of Nuclear Physics, and a visiting Professor of Economics at the Indian Statistical Institute. He has research interests in statistical physics, condensed matter physics, computational physics and econophysics. anirban chakraborti is an Associate Professor at the Quantitative Finance Group,École Centrale Paris. He has research interests in statistical physics, econophysics and quantum physics. satya r. chakravarty is a Professor in the Economic Research Unit of the Indian Statistical Institute. His main areas of research interests are welfare economics, public economics, mathematical finance, industrial organization and game theory. arnab chatterjee is a Postdoctoral Researcher at Aalto University. He has research interests in statistical physics, and its application to condensed matter and social sciences.

Structural properties of the Indian Railway network is studied in the light of recent investigations of the scaling properties of different complex networks. Stations are considered as 'nodes' and an arbitrary pair of stations is said to be connected by a 'link' when at least one train stops at both stations. Rigorous analysis of the existing data shows that the Indian Railway network displays small-world properties. We define and estimate several other quantities associated with this network. Given a chance, how would we have possibly organized our train travel? People dislike to change trains to reach their destinations. Therefore an extreme possibility would be to run a single train passing through all stations in the country so that no change of train is needed at all! An obvious disadvantage in this strategy is that the average distance between the stations become very large and so also the time needed for travel. The other limiting situation would be, to run a train between any pair of neighbouring stations and try to travel along the minimal paths. This requires a change of train at every station, which is also clearly not economically viable. Railway networks in no country in the world follow either of the two ways, actually they go mid-way. Like any other transport system the main motivation of railways is to be fast and economic. To achieve it, railways run simultaneously many trains, covering short as well as long routes so that a traveller does not need to change more than only a few trains to reach any arbitrary destination in the country.In this paper we analyse the structure of the Indian Railway network (IRN). This is done in the context of recent investigations of the scaling properties of several complex networks e.g., social, biological, computational networks [1] etc. Identifying the stations as nodes of the network and a train which stops at any two stations as the link between the nodes we measure the average distance between an arbitrary pair of stations and find that it depends only logarithmically on the total number of stations in the country. While from the network point of view this implies the small-world nature of the railway network, in practice a traveller has to change only few trains to reach an arbitrary destination. This implies that over years, the railway network has been evolved with the sole aim in mind to make it fast and economic, eventually its structure has become a small-world network [2].The structure and properties of several social, biological and computational networks like the World-wide web (WWW) [3]

Abstract. Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium. However, it also deviates in the low income and more significantly for the high income ranges. Application of physics models provides illuminating ideas and understanding, complementing the observations.

We propose a model of continuous opinion dynamics, where mutual interactions can be both positive and negative. Different types of distributions for the interactions, all characterized by a single parameter $p$ denoting the fraction of negative interactions, are considered. Results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p=p_c below which a consensus is reached. Although the order-disorder transition is analogous to a ferromagnetic-paramagnetic phase transition with comparable critical exponents, the model is characterized by some distinctive features relevant to a social system.Comment: 10 pages, 5 eps fig