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

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.

Geometrical Derivation of Equilibrium Distributions in Some Stochastic Systems

“…(16), we obtain the Boltzmann distribution (9) in the limit N → ∞ (which also implies E → ∞). This asymptotic result reproduces the distribution of real economic data [10] and also the results obtained in several models of economic agents with deterministic, random or chaotic exchange interactions [6,12,13].…”

“…In some cases, it can be reached by random forces [6], in other cases by chaotic [13,19] or deterministic [12] causes. Evidently, the proof that these mechanisms generate equiprobability is not a trivial task and it remains as a typical challenge in this kind of problems.…”

Competitively coupled maps and spatial pattern formation

“…Although the model studied in these papers is formally similar to our model, the aims of our work and that of Refs. [20][21][22] are very different. Whereas our focus is on how a homogeneous initial state can undergo spontaneous symmetry breaking and result in stable pattern formation, Refs.…”

“…[20][21][22] in the context of understanding income distributions. Although the model studied in these papers is formally similar to our model, the aims of our work and that of Refs.…”

“…Whereas our focus is on how a homogeneous initial state can undergo spontaneous symmetry breaking and result in stable pattern formation, Refs. [20][21][22] do not contain any discussion of spatial pattern formation and are, instead, concerned with modeling wealth or income distributions in society.…”