Transition from Pareto to Boltzmann–Gibbs behavior in a deterministic economic model

The one-dimensional deterministic economic model recently studied by González-Estévez et al. [J. González-Estévez, M.G. Cosenza, R. López-Ruiz, J.R. Sanchez, Physica A 387 (2008) 4637] is considered on a two-dimensional square lattice with periodic boundary conditions. In this model, the evolution of each agent is described by a map coupled with its nearest neighbors. The map has two factors: a linear term that accounts for the agent’s own tendency to grow and an exponential term that saturates this growth through the control effect of the environment. The regions in the parameter space where the system displays Pareto and Boltzmann–Gibbs statistics are calculated for the cases of the von Neumann and the Moore neighborhood. It is found that, even when the parameters in the system are kept fixed, a transition from Pareto to Boltzmann–Gibbs behavior can occur when the number of neighbors of each agent increases.