Related papers: Explicit equilibria in a kinetic model of gambling
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through the binary trades introduced in Cordier, Pareschi,…
We briefly review results on nonlinear kinetic equation of Boltzmann type which describe the evolution of wealth in a simple agents market. The mathematical structure of the underlying kinetic equations allows to use well-known techniques…
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 discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown…
Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in…
An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of…
In this work we consider an agent based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero sum game. Simultaneously, the agents update their way of play trying to learn the…
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…
This note explains why a large class of fair, or reversible "money games", i.e., stochastic models of wealth redistribution among agents, lead to steady states described by canonical and microcanonical distributions. The games considered…
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…
We study the dynamics of individual agents in some kinetic models of wealth exchange, particularly, the models with savings. For the model with uniform savings, agents perform simple random walks in the "wealth space". On the other hand, 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…
Binary kinetic exchange models, where money is shuffled between two agents at a time, reproduce the Boltzmann Gibbs exponential wealth distribution but cannot address the multi party trades common in real markets. We generalize the exchange…
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete…
We develop a general framework, based on Boltzmann transport theory, to analyze the distribution of wealth in societies. Within this framework we derive the distribution function of wealth by using a two-party trading model for the poor…
We propose a kinetic model to describe the dynamical evolution of wealth and knowledge in national and global markets, starting from a microscopic description of individual interactions. The model is built upon interaction rules that…
A class of conserved models of wealth distributions are studied where wealth (or money) is assumed to be exchanged between a pair of agents in a population like the elastically colliding molecules of a gas exchanging energy. All sorts of…
An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy changes…
The "Money Exchange Model" is a type of agent-based simulation model used to study how wealth distribution and inequality evolve through monetary exchanges between individuals. The primary focus of this model is to identify the limiting…
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…