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Register a new userExchanges in complex networks: income and wealth distributions
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We investigate the wealth evolution in a system of agents that exchange wealth through a disordered network in presence of an additive stochastic Gaussian noise. We show that the resulting wealth distribution is shaped by the degree distribution of the underlying network and in particular we verify that scale free networks generate distributions with power-law tails in the high-income region. Numerical simulations of wealth exchanges performed on two different kind of networks show the inner relation between the wealth distribution and the network properties and confirm the agreement with a self-consistent solution. We show that empirical data for the income distribution in Australia are qualitatively well described by our theoretical predictions.
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We analyze the cumulative distribution of total personal income of USA counties, and gross domestic product of Brazilian, German and United Kingdom counties, and also of world countries. We verify that generalized exponential distributions, related to nonextensive statistical mechanics, describe almost the whole spectrum of the distributions (within acceptable errors), ranging from the low region to the middle region, and, in some cases, up to the power-law tail. The analysis over about 30 years (for USA and Brazil) shows a regular pattern of the parameters appearing in the present phenomenological approach, suggesting a possible connection between the underlying dynamics of (at least some aspects of) the economy of a country (or of the whole world) and nonextensive statistical mechanics. We also introduce two additional examples related to geographical distributions: land areas of counties and land prices, and the same kind of equations adjust the data in the whole range of the spectrum.
Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a fair market, the wealth distribution among individual investors fulfills a power law. We then argue that fair play for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent $alpha sim 3/2$. In particular we relate it to the average number of individuals L depending on the average wealth: $alpha sim L/(L-1)$. Then we connect it to certain power exponents characterising the stock markets. We obtain that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent $beta sim alpha sim 3/2$. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order $gamma sim 2 alpha sim 3$. These results are consistent with recent experimental measurements of these power law exponents ([Maslov 2001] for $beta$ and [Gopikrishnan et al. 1999] for $gamma$).
Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community - income inequality. We propose a new method to study the scaling of income distributions by analyzing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyze the shapes of income distributions. First, we find that mean, variance, skewness, and kurtosis of income distributions all increase with city size. Second, the Kullback-Leibler divergence between a citys income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.
A model of communication that is able to cope simultaneously with the problems of search and congestion is presented. We investigate the communication dynamics in model networks and introduce a general framework that enables a search of optimal structures.
An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of money has recently been proposed by one of us (RLR). This equation takes the form of an iterated nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.
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