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We propose a novel kinetic exchange model differing from previous ones in two main aspects. First, the basic dynamics is modified in order to represent economies where immediate wealth exchanges are carried out, instead of reshufflings or…
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…
This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that…
Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global…
We propose a stochastic model of evolution of wealth in a society of economic agents. In the model, an agent can be in two states: inactive and active. Transitions between the states occur at random time intervals. In the active state, the…
We propose and investigate general kinetic models %of Boltzmann type with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. These models can be applied to many…
The so-called "Yard-Sale Model" of wealth distribution posits that wealth is transferred between economic agents as a result of transactions whose size is proportional to the wealth of the less wealthy agent. In recent work [B.M. Boghosian,…
A dynamical model of capital exchange is introduced in which a specified amount of capital is exchanged between two individuals when they meet. The resulting time dependent wealth distributions are determined for a variety of exchange…
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…
We study two kinds of economic exchange, additive and multiplicative, in a system of N agents. The work is divided in two parts, in the first one, the agents are free to interact with each other. The system evolves to a Boltzmann-Gibbs…
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…
Aiming to describe the wealth distribution evolution, several models consider an ensemble of interacting economic agents that exchange wealth in binary fashion. Intriguingly, models that consider an unbiased market, that gives to each agent…
The Kinetic Gas Theory like two-agent money exchange models, recently introduced in the Econophysics of Wealth distributions, are revisited. The emergence of Boltzmann-Gibbs like distribution of individual money to Pareto's law in the tail…
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic…
Homogeneous Boltzmann-type equations are an established tool for modelling interacting multi-agent systems in sociophysics by means of the principles of statistical mechanics and kinetic theory. A customary implicit assumption is that…
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…
We investigate the unbiased model for money exchanges: agents give at random time a dollar to one another (if they have one). Surprisingly, this dynamics eventually leads to a geometric distribution of wealth (shown empirically by…
How do individuals accumulate wealth as they interact economically? We outline the consequences of a simple microscopic model in which repeated pairwise exchanges of assets between individuals build the wealth distribution of a population.…
Simple agent based exchange models are a commonplace in the study of wealth distribution of artificial societies. Generally, each agent is characterized by its wealth and by a risk-aversion factor, and random exchanges between agents allow…
The temporal evolution of a contagious viral disease is modelled as the dynamic progression of different classes of population with individuals interacting pairwise. This interaction follows a binary mechanism typical of kinetic theory,…