Related papers: Nonequilibrium statistical mechanics of money/ener…
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…
This Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the…
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the…
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 discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we show its functional…
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…
We investigate the uniform reshuffling model for money exchanges: two agents picked uniformly at random redistribute their dollars between them. This stochastic dynamics is of mean-field type and eventually leads to a exponential…
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…
We present a novel reshuffling exchange model and investigate its long time behavior. In this model, two individuals are picked randomly, and their wealth $X_i$ and $X_j$ are redistributed by flipping a sequence of fair coins leading to a…
Fair division is a significant, long-standing problem and is closely related to social and economic justice. The conventional division methods such as cut-and-choose are hardly applicable to realworld problems because of their complexity…
Models in econophysics, i.e., the emerging field of statistical physics that applies the main concepts of traditional physics to economics, typically consist of large systems of economic agents who are characterized by the amount of money…
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…
The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…
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…
Simple stochastic exchange games are based on random allocation of finite resources. These games are Markov chains that can be studied either analytically or by Monte Carlo simulations. In particular, the equilibrium distribution can be…
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…
This paper is concerned with general spatially explicit versions of three stochastic models for the dynamics of money that have been introduced and studied numerically by statistical physicists: the uniform reshuffling model, the immediate…
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…