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The kinetic exchange model has gained popularity in the field of statistical mechanics for investigating wealth interaction. Traditionally, kinetic exchange models have been studied without considering preferential interactions. However, in…
Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the…
Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a…
To gain insights into the problem of regional inequality, we proposed new regional asset exchange models based on existing kinetic income-exchange models in economic physics. We did this by setting the spatial exchange range and adding bias…
Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock…
We present a stylized model with feedback loops for the evolution of a population's wealth over generations. Individuals have both talent and wealth: talent is a random variable distributed identically for everyone, but wealth is a random…
We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time…
This paper attempts to find a relationship between agents' risk aversion and inequality of incomes. Specifically, a model is proposed for the evolution in time of surplus/deficit distribution, and the long-time distributions are…
In order to describe the properties of the observed distribution of wealth in a population, most economic models rely on the existence of an asymptotic equilibrium state. In addition, the process generating the equilibrium distribution is…
We develop a mathematical framework to study the economic impact of infectious diseases by integrating epidemiological dynamics with a kinetic model of wealth exchange. The multi-agent description leads to study the evolution over time of a…
The distribution of money is analysed in connection with the Boltzmann distribution of energy in the degenerate states of molecules. Plots of the population density of income distribution for various countries are well reproduced by a Gamma…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
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…
We develop a statistical framework for wealth allocation in which agents hold discrete units of wealth and macrostates are defined by how wealth is distributed across agents. The structure of the economic state space is characterized…
We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. In analogy to statistical systems in equilibrium, money and the average money per economic agent are…
Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between $n$ economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background,…
This paper reviews recent attempts at modelling inequality of wealth as an emergent phenomenon of interacting-agent processes. We point out that recent models of wealth condensation which draw their inspiration from molecular dynamics have,…
In several recent works on infinite-dimensional systems of ODEs \cite{cao_derivation_2021,cao_explicit_2021,cao_iterative_2024,cao_sticky_2024}, which arise from the mean-field limit of agent-based models in economics and social sciences…
A simple computer simulation model of a closed market on a fixed network with free flow of goods and money is introduced. The model contains only two variables : the amount of goods and money beside the size of the system. An initially flat…
We consider a model of power distribution in a social system where a set of agents play a simple game on a graph: the probability of winning each round is proportional to the agent's current power, and the winner gets more power as a…