Why only few are so successful ?

In many professons employees are rewarded according to their relative performance. Corresponding economy can be modeled by taking $N$ independent agents who gain from the market with a rate which depends on their current gain. We argue that this simple realistic rate generates a scale free distribution even though intrinsic ability of agents are marginally different from each other. As an evidence we provide distribution of scores for two different systems (a) the global stock game where players invest in real stock market and (b) the international cricket.Comment: 8 pages, 3 eps figures, elsart.cls (included), accepted in Physica

Living in an Irrational Society: Wealth Distribution with Correlations between Risk and Expected Profits

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer agent in a transaction. Here we study the case where the partners in the transaction have a previous knowledge of the winning probability and adjust their risk aversion taking this information into consideration. The results indicate that a relatively equalitarian society is obtained when the agents risk in direct proportion to their winning probabilities. However, it is the opposite case that delivers wealth distribution curves and Gini indices closer to empirical data. This indicates that, at least for this very simple model, either agents have no knowledge of their winning probabilities, either they exhibit an ``irrational'' behavior risking more than reasonable.Comment: 7 pages, 8 figure

Economic exchanges in a stratified society: End of the middle class?

We study the effect of the social stratification on the wealth distribution on a system of interacting economic agents that are constrained to interact only within their own economic class. The economical mobility of the agents is related to its success in exchange transactions. Different wealth distributions are obtained as a function of the width of the economic class. We find a range of widths in which the society is divided in two classes separated by a deep gap that prevents further exchange between poor and rich agents. As a consequence, the middle wealth class is eliminated. The high values of the Gini indices obtained in these cases indicate a highly unequal society. On the other hand, lower and higher widths induce lower Gini indices and a fairer wealth distribution.Comment: 7 pages, 2 figures, 1 table, to appear in Physica

Evidence for the exponential distribution of income in the USA

Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. From the individual income distribution, we derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8=0.375 calculated for two-earners families.Comment: 4 pages, including 5 figures. Uses Springer Verlag style classes for Eur. Phys. J. B (included). Submitted to the proceedings of APFA2 conference. V.2: minor stylistic improvement

Dynamics of Money and Income Distributions

We study the model of interacting agents proposed by Chatterjee et al that allows agents to both save and exchange wealth. Closed equations for the wealth distribution are developed using a mean field approximation. We show that when all agents have the same fixed savings propensity, subject to certain well defined approximations defined in the text, these equations yield the conjecture proposed by Chatterjee for the form of the stationary agent wealth distribution. If the savings propensity for the equations is chosen according to some random distribution we show further that the wealth distribution for large values of wealth displays a Pareto like power law tail, ie P(w)\sim w^{1+a}. However the value of $a$ for the model is exactly 1. Exact numerical simulations for the model illustrate how, as the savings distribution function narrows to zero, the wealth distribution changes from a Pareto form to to an exponential function. Intermediate regions of wealth may be approximately described by a power law with $a>1$. However the value never reaches values of \~ 1.6-1.7 that characterise empirical wealth data. This conclusion is not changed if three body agent exchange processes are allowed. We conclude that other mechanisms are required if the model is to agree with empirical wealth data.Comment: Sixteen pages, Seven figures, Elsevier style file. Submitted to Physica

Correlation between Risk Aversion and Wealth distribution

Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's wealth power law distribution. One important factor to be considered is the existence of risk aversion. In this paper we study a model where agents posses different levels of risk aversion, going from uniform to a random distribution. In all cases the risk aversion level for a given agent is constant during the simulation. While for a uniform and constant risk aversion the system self-organizes in a distribution that goes from an unfair ``one takes all'' distribution to a Gaussian one, a random risk aversion can produce distributions going from exponential to log-normal and power-law. Besides, interesting correlations between wealth and risk aversion are found.Comment: 8 pages, 7 figures, submitted to Physica A, Proceedings of the VIII LAWNP, Salvador, Brazil, 200

Emergence of Power Law in a Market with Mixed Models

We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A yardsale(YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud(TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, {\it i.e.} there are some agents following TF model while rest follow YS model, it leads to distribution with power law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power law tail in wealth distribution if we allow the agents to follow either of the models with some probability.Comment: 18 pages and 9 figure

Statistical mechanics of money

In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. We demonstrate how the Gibbs distribution emerges in computer simulations of economic models. Then we consider a thermal machine, in which the difference of temperatures allows one to extract a monetary profit. We also discuss the role of debt, and models with broken time-reversal symmetry for which the Gibbs law does not hold.Comment: 7 pages, 5 figures, RevTeX. V.4: final version accepted to Eur. Phys. J. B: few stylistic revisions and additional reference