In this work we study the individual strategies carried out by agents undergoing transactions in wealth exchange models. We analyze the role of risk propensity in the behavior of the agents and find a critical risk, such that agents with risk above that value always end up losing everything when the system approaches equilibrium. Moreover, we find that the wealth of the agents is maximum for a range of risk values that depends on particular characteristics of the model, such as the social protection factor. Our findings allow to determine a region of parameters for which the strategies of the economic agents are successful.
Given the wealth inequality worldwide, there is an urgent need to identify the mode of wealth exchange through which it arises. To address the research gap regarding models that combine equivalent exchange and redistribution, this study compares an equivalent market exchange with redistribution based on power centers and a nonequivalent exchange with mutual aid using the Polanyi, Graeber, and Karatani modes of exchange. Two new exchange models based on multi-agent interactions are reconstructed following an econophysics approach for evaluating the Gini index (inequality) and total exchange (ec…
How can we limit wealth disparities while stimulating economic flows in sustainable societies? To examine the link between these concepts, we propose an econophysics asset exchange model with the surplus stock of the wealthy. The wealthy are one of the two exchange agents and have more assets than the poor. Our simulation model converts the surplus contribution rate of the wealthy to a new variable parameter alongside the saving rate and introduces the total exchange (flow) and rank correlation coefficient (metabolism) as new evaluation indexes, adding to the Gini index (disparities), thereby …
Islamic and capitalist economies have several differences, the most fundamental being that the Islamic economy is characterized by the prohibition of interest (riba) and speculation (gharar) and the enforcement of Shariah-compliant profit-loss sharing (mudaraba, murabaha, salam, etc.) and wealth redistribution (waqf, sadaqah, and zakat). In this study, I apply new econophysics models of wealth exchange and redistribution to quantitatively compare these characteristics to those of capitalism and evaluate wealth distribution and disparity using a simulation. Specifically, regarding exchange, I p…
We study analytically the change in the wealth ($x$) distribution $P(x)$ against saving propensity $λ$ in a closed economy, using the Kinetic theory. We estimate the Gini ($g$) and Kolkata ($k)$ indices by deriving (using $P(x)$) the Lorenz function $L(f)$, giving the cumulative fraction $L$ of wealth possessed by fraction $f$ of the people ordered in ascending order of wealth. First, using the exact result for $P(x)$ when $λ= 0$ we derive $L(f)$, and from there the index values $g$ and $k$. We then proceed with an approximate gamma distribution form of $P(x)$ for non-zero values of $λ$. Then …
In the manuscript, we are interested in using kinetic theory to better understand the time evolution of wealth distribution and their large scale behavior such as the evolution of inequality (e.g. Gini index). We investigate three type of dynamics denoted unbiased, poor-biased and rich-biased dynamics. At the particle level, one agent is picked randomly based on its wealth and one of its dollar is redistributed among the population. Proving the so-called propagation of chaos, we identify the limit of each dynamics as the number of individual approaches infinity using both coupling techniques […
The agent-based Yard-Sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a parameter $λ$. Our numerical results indicate that the model has a critical point at $λ=1$ between a phase for $λ< 1$ with economic mobility and exponentially growing wealth of all agents and a non-stationary phase for $λ\geq 1$ with wealth condensation and no mobility. We define the energy of the system and show that the system can be considered to be in thermod…
A new $κ$-deformed parametric model for the size distribution of wealth
Patriarca et al.（2005）指出，具有分布式储蓄参数的非均质动力学交换模型中的幂律尾均衡分布可以分解为对应于特定代理子集的Gamma分布的混合。在这里，我们提出了一个新的四参数统计分布，这是一个$κ$变形的广义伽玛分布的幂律尾部，基于变形的指数和对数函数Kaniadakis（2001）。我们发现，这个新的分布也是一个扩展的$κ$ -广义分布提出的Clementi等。（2007），与一个额外的形状参数$ν$，并正确地再现了整个范围内的财富分布在这样的异质动力学交换模型。我们还提供了各种相关的统计措施和不平等措施。
Relations Among Different Inequality Measures in Complex Systems: From Kinetic Exchange to Earthquake Models
Indian Institute of Science Education and Research（印度科学教育研究所）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Indian Statistical Institute（印度统计研究所）；Saha Institute of Nuclear Physics（萨哈核物理研究所）
We develop a mean-field theory of the growth, exchange and distribution (GED) model introduced by Kang et al. (preceding paper) that accurately describes the phase transition in the limit that the number of agents $N$ approaches infinity. The GED model is a generalization of the Yard-Sale model in which the additional wealth added by economic growth is nonuniformly distributed to the agents according to their wealth in a way determined by the parameter $λ$. The model was shown numerically to have a phase transition at $λ=1$ and be characterized by critical exponents and critical slowing down. …
Limiting risk to reduce inequality: insights from the Yard-Sale model
Centro Atómico Bariloche (CNEA)（巴里洛切原子中心）；CONICET（阿根廷国家科学研究委员会）；Instituto Balseiro, Universidad Nacional de Cuyo（门多萨国立大学巴尔塞罗研究所）；Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）
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。
