Pareto and Boltzmann-Gibbs behaviors in a deterministic multi-agent system

TL;DR

This paper investigates a deterministic multi-agent system modeling economic dynamics, revealing conditions under which the system exhibits Pareto or Boltzmann-Gibbs statistical behaviors and analyzing wealth distribution properties.

Contribution

It introduces a coupled map lattice model for economic agents and identifies parameter regions leading to different statistical behaviors, including wealth distribution analysis.

Findings

System exhibits Pareto or Boltzmann-Gibbs behaviors depending on parameters.

Wealth distribution metrics vary systematically with model parameters.

Parameter regions for different statistical regimes are mapped.

Abstract

A deterministic system of interacting agents is considered as a model for economic dynamics. The dynamics of the system is described by a coupled map lattice with near neighbor interactions. The evolution of each agent results from the competition between two factors: the agent's own tendency to grow and the environmental influence that moderates this growth. Depending on the values of the parameters that control these factors, the system can display Pareto or Boltzmann-Gibbs statistical behaviors in its asymptotic dynamical regime. The regions where these behaviors appear are calculated on the space of parameters of the system. Other statistical properties, such as the mean wealth, the standard deviation, and the Gini coefficient characterizing the degree of equity in the wealth distribution are also calculated on the space of parameters of the system.