Related papers: Breakdown of the mean-field approximation in a wea…
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.…
This article reviews a few basic features of systems of one-dimensional diffusions with rank-based characteristics. Such systems arise in particular in the modelling of financial markets , where they go by the name of Atlas models. We…
The inequality of wealth distribution is a universal phenomenon in the civilized nations, and it is often imputed to the Matthew effect, that is, the rich get richer and the poor get poorer. Some philosophers unjustified this phenomenon and…
In this short paper we define the wealth process in a spin model for market microstructure, for individual agents and in aggregate. The agents in our model try to balance their desire to belong to the local majority (herding behavior),…
The conservative wealth-exchange process derived from trade interactions is modeled as a multiplicative stochastic transference of value, where each interaction multiplies the wealth of the poorest of the two intervening agents by a random…
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,…
We investigate a variant of the standard Bennati-Dragulescu-Yakovenko (BDY) game \cite{dragulescu_statistical_2000} inspired by the very recent work \cite{blom_hallmarks_2024}, where agents involving in a money exchange dynamics are…
This paper investigates the emergence of wealth inequality through a minimalist kinetic exchange model that incorporates two fundamental economic features: fixed-amount transactions and hard budget constraints. In contrast to the maximum…
Many models of market dynamics make use of the idea of wealth exchanges among economic agents. A simple analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the energy exchange…
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general…
We introduce a mean-field type approximation for description of company's income statistics. Utilizing huge company data we show that a discrete version of Langevin equation with additive and multiplicative noises can appropriately describe…
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong…
We study the wealth distribution of UK households through a detailed analysis of data from wealth surveys and rich lists, and propose a non-linear Kesten process to model the dynamics of household wealth. The main features of our model are…
A generalized continuous economic model is proposed for random markets. In this model, agents interact by pairs and exchange their money in a random way. A parameter controls the effectiveness of the transactions between the agents. We show…
We analyze inequality aspects of the agent-based model of capitalist economy named it Social Architecture of Capitalism that has been introduced by Ian Wright. The model contemplates two main types of agents, workers and capitalists, which…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
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…
The aim of this paper is to propose a heterogeneous agent model of stock markets that develop complicated endogenous price fluctuations. We find occurrences of non-stationary chaos, or speculative bubble, are caused by the heterogeneity of…
Social and economic inequality is a plague of the XXI Century. It is continuously widening, as the wealth of a relatively small group increases and, therefore, the rest of the world shares a shrinking fraction of resources. This situation…
This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…