Some general features of kinetic multi-agent models are reviewed, with particular attention to the relation between the agent saving propensities and the form of the equilibrium wealth distribution. The effect of a finite cutoff of the saving propensity distribution on the corresponding wealth distribution is studied. Various results about kinetic multi-agent models are collected and used to construct a realistic wealth distribution with zero limit for small values of wealth, an exponential form at intermediate and a power law tail at larger values of wealth.
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…
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 …
The lattice gas automaton (LGA) is proposed for a closed economic market of agents with heterogeneous saving interests. There are two procedures in the standard LGA, i.e., "propagation" + "transaction". If the propagation step is removed and the transaction is conducted among all agents, the LGA reduces to a more simplified kinetic model. In addition, two dealing rules are imposed on the transaction phase. Under Rule I, the trading volume depends on the average saving propensities of an arbitrary pair of agents in trade. Under Rule II, the exchange is governed by a stochastic parameter between…
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 …
It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of Gamma distributions corresponding to particular subsets of agents. Here, we propose a new four-parameter statistical distribution which is a $κ$-deformation of the Generalized Gamma distribution with a power-law tail, based on the deformed exponential and logarithm functions introduced by Kaniadakis(2001). We found that this new distribution is also an extension to the $κ$-Generalized d…
Empirical distributions of wealth and income can be reproduced using simplified agent-based models of economic interactions, analogous to microscopic collisions of gas particles. Building upon these models of freely interacting agents, we explore the effect of a segregated economic network in which interactions are restricted to those between agents of similar wealth. Agents on a 2D lattice undergo kinetic exchanges with their nearest neighbours, while continuously switching places to minimize local wealth differences. A spatial concentration of wealth leads to a steady state with increased gl…
We propose in this work a kinetic wealth-exchange model of economic growth by introducing saving as a non consumed fraction of production. In this new model, which starts also from microeconomic arguments, it is found that economic transactions between pairs of agents leads the system to a macroscopic behavior where total wealth is not conserved and it is possible to have an economic growth which is assumed as the increasing of total production in time. This last macroeconomic result, that we find both numerically through a Monte Carlo based simulation method and analytically in the framework …
We report the numerical results for the steady state income or wealth distribution $P(m)$ and the resulting inequality measures (Gini $g$ and Kolkata $k$ indices) in the kinetic exchange models of market dynamics. We study the variations of $P(m)$ and of the indices $g$ and $k$ with the saving propensity $λ$ of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest o…
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）
