A model of distribution of the wealth in a society based on the properties of complex networks has been proposed. The wealth is interpreted as a consequence of communication possibilities and proportional to the number of connections possessed by a person (as a vertex of the social network). Numerical simulation of wealth distribution shows a transition from the Pareto law to distribution with a gap demonstrating the absence of the middle class. Such a transition has been described as a second-order phase transition, the order parameter has been introduced and the value of the critical exponent has been found.
Fokker-Planck Description of Wealth Dynamics and the Origin of Pareto's Law
所谓的财富分配的“庭院销售模型”假定，财富在经济主体之间转移是交易的结果，交易的规模与较不富裕的主体的财富成正比。在最近的工作中[B]。Boghosian，“Kinetics of Wealth and the Pareto Law”，{ \it Phys. Rev. E} { \bf 89}（2014）042804]，表明这导致了支配财富分配的福克-普朗克方程。随着财富再分配机制的增加，进一步表明，该模型导致了在形式上与帕累托定律非常相似的固定财富分配。本文给出了该Fokker-Planck方程的一种更为简单的推导方法。
Understanding of evolutionary mechanism of online social networks is greatly significant for the development of network science. However, present researches on evolutionary mechanism of online social networks are neither deep nor clear enough. In this study, we empirically showed the essential evolution characteristics of Renren online social network. From the perspective of Pareto wealth distribution and bidirectional preferential attachment, the origin of online social network evolution is analyzed and the evolution mechanism of online social networks is explained. Then a novel model is prop…
Using the empirical data from the Norwegian tax office, we analyse the wealth and income of the richest individuals in Norway during the period 2010--2013. We find that both annual income and wealth level of the richest individuals are describable using the Pareto law. We find that the robust mean Pareto exponent over the four-year period to be $\approx 2.3$ for income and $\approx 1.5$ for wealth.
A Unified Framework for the Pareto Law and Matthew Effect using Scale-Free Networks
我们采用进化博弈的方式研究了无标度网络中的累积财富分布。该系统自组织到一个临界帕累托分布（1897）的财富$P(m)\sim m^{-(v+1)}$与$1.6 < v <2.0$（这是在协议与美国或日本）。特别是，代理人的个人财富与其联系人数量成正比这种现象与社会、经济、科学等领域中存在的马太效应相吻合。虽然我们的模型比较简单，但它很好地代表了经济中的合作和利润积累行为，它将网络理论与经济物理学相结合。
We consider a simple theoretical model to investigate the impact of inheritances on the wealth distribution. Wealth is described as a finite resource, which remains constant over different generations and is divided equally among offspring. All other sources of wealth are neglected. We consider different societies characterized by a different offspring probability distribution. We find that, if the population remains constant, the society reaches a stationary wealth distribution. We show that inequality emerges every time the number of children per family is not always the same. For realistic …
Income and wealth distribution affect stability of a society to a large extent and high inequality affects it negatively. Moreover, in the case of developed countries, recently has been proven that inequality is closely related to all negative phenomena affecting society. So far, Econophysics papers tried to analyse income and wealth distribution by employing distributions such as Fermi-Dirac, Bose-Einstein, Maxwell-Boltzmann, lognormal (Gibrat), and exponential. Generally, distributions describe mostly income and less wealth distribution for low and middle income segment of population, which …
Thermodynamic description of wealth inequality in the world
1 Univ Toulouse, CNRS, Laboratoire de Physique Th\'eorique, Toulouse, France 2 Departamento de F\' sica Te\'orica, GIyA, Comisi\'on Nacional de Energ\' a At\'omica. Av. del Libertador 8250, 1429 Buenos Aires, Argentina
In earlier work, we derived a nonlinear, nonlocal Fokker-Planck equation for the Yard-Sale Model of asset exchange. In the absence of redistribution, we showed that the Gini coefficient is a Lyapunov functional for this model, tending to one in the time-asymptotic limit, corresponding to maximal inequality. When a one-parameter model of redistribution is introduced, we showed that the model admits a steady state similar to Pareto's Law. In this work, we analyze the form of this distribution in greater detail, both analytically and numerically. We find that, while Pareto's Law is approximately …
A mean-field like stochastic evolution equation with growth and reset terms (LGGR model) is used to model wealth distribution in modern societies. The stationary solution of the model leads to an analytical form for the density function that is successful in describing the observed data for all wealth categories. In the limit of high wealth values the proposed density function has the accepted Tsallis-Pareto shape. Our results are in agreement with the predictions of an earlier approach based on a mean-field like wealth exchange process.
Socio-economic inequalities derived from an exhaustive wealth distribution is studied in a closed geographical region from Transylvania (Romania). Exhaustive wealth data is computed from the agricultural records of the Sancraiu commune for three different economic situations. The gathered data is spanning two different periods from the communist economy and the present situation after 31 years of free market economy in Romania. The local growth and reset model based on an analytically solvable master equation is used to describe the observed data. The model with realistically chosen growth and…
We introduce a class of new one-dimensional linear Fokker--Planck type equations describing the evolution in time of the wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker--Planck equations remains unchanged with respect to the steady state of the original Fokker--Planck equation. However, unlike the original equation, it…
Universidade de São Paulo（圣保罗大学）；The Abdus Salam International Centre For Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；UNAM（墨西哥国立自治大学）；International School for Advanced Studies (SISSA)（高级研究国际学院）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
Role of Selective Interaction in Wealth Distribution
在我们的简化描述中，“财富”就是金钱（$m$）。研究了一种类似气体的货币模型的动力学理论，其中两个代理人选择性地相互作用（交易），并在他们之间交换一定数量的货币，使得他们的货币总和不变，从而所有代理人的总货币保持守恒。单个货币的概率分布（$P(m)$ vs. $m$）被认为受到某些选择性相互作用方式的影响。分布偏离玻尔兹曼-吉布斯指数分布，在某些情况下，分布出现幂律尾部，称为帕累托定律（$P(m) \propto m^{-(1+α)}$）。幂律在其他一些密切相关的守恒和离散模型中也得到了观察。讨论提供了数值支持，有一个挖掘到出现的幂律在这样的模型。
In this work, we modify the affine wealth model of wealth distributions to examine the effects of nonconstant redistribution on the very wealthy. Previous studies of this model, restricted to flat redistribution schemes, have demonstrated the presence of a phase transition to a partially wealth-condensed state, or "partial oligarchy," at the critical value of an order parameter. These studies have also indicated the presence of an exponential tail in wealth distribution precisely at criticality. Away from criticality, the tail was observed to be Gaussian. In this work, we generalize the flat r…
The spreading of Covid-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modelling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth dist…
We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We are mainly interested in interactions increasing wealth inequality that is in a local implementation of the accumulated advantage principle. Such interactions destabilise the system. They are confronted in the model with a global regulatory mechanism which reduces wealth inequality. There are different scenarios emerging as a net effect of these two competin…
The dynamics of wealth distribution plays a critical role in the economic market, hence an understanding of its nonequilibrium statistical mechanics is of great importance to human society. For this aim, a simple and efficient one-dimensional (1D) lattice gas automaton (LGA) is presented for wealth distribution of agents with or without saving propensity. The LGA comprises two stages, i.e., random propagation and economic transaction. During the former phase, an agent either remains motionless or travels to one of its neighboring empty sites with a certain probability. In the subsequent proced…
This paper presents a physical perspective on the human migration phenomenon claiming that human social behaviors are somehow but not completely inspired by nature. Human displacement or migration in the world is highly affected by equivalent weighted wealth and multidimensional poverty distribution across countries. In this work, it has been shown that the equivalent weighted wealth as an important characteristic of a society can be introduced in a mathematical language in terms of a country gross productivity factor, safety and social factors, environmental and economic factors, political an…
The uneven distribution of wealth and individual economic capacities are among the main forces which shape modern societies and arguably bias the emerging social structures. However, the study of correlations between the social network and economic status of individuals is difficult due to the lack of large-scale multimodal data disclosing both the social ties and economic indicators of the same population. Here, we close this gap through the analysis of coupled datasets recording the mobile phone communications and bank transaction history of one million anonymised individuals living in a Lat…
Families form the basis of society, and anthropologists have characterised various family systems. This study developed a multi-level evolutionary model of pre-industrial agricultural societies to simulate the evolution of family systems and determine how each of them adapts to environmental conditions and forms a characteristic socio-economic structure. In the model, competing societies evolve, which themselves comprise multiple evolving families that grow through family labour. Each family has two strategy parameters: the time children leave the parental home and the distribution of inherita…
We study a system of $N$ agents, whose wealth grows linearly, under the effect of stochastic resetting and interacting via a tax-like dynamics -- all agents donate a part of their wealth, which is, in turn, redistributed equally among all others. This mimics a socio-economic scenario where people have fixed incomes, suffer individual economic setbacks, and pay taxes to the state. The system always reaches a stationary state, which shows a trivial exponential wealth distribution in the absence of tax dynamics. The introduction of the tax dynamics leads to several interesting features in the sta…
A brief overview of the models and data analyses of income, wealth, consumption distributions by the physicists, are presented here. It has been found empirically that the distributions of income and wealth possess fairly robust features, like the bulk of both the income and wealth distributions seem to reasonably fit both the log-normal and Gamma distributions, while the tail of the distribution fits well to a power law (as first observed by sociologist Pareto). We also present our recent studies of the unit-level expenditure on consumption across multiple countries and multiple years, where …
