Eur. Phys. J. Special Topics 225, 1879-1891 (2016)
https://doi.org/10.1140/epjst/e2015-50119-6

Regular Article

Discretized kinetic theory on scale-free networks

Faculty of Science and Technology, Free University of Bozen-Bolzano, Bolzano, Italy

^a e-mail: giovanni.modanese@unibz.it

Received: 13 June 2015
Revised: 10 January 2016
Published online: 26 October 2016

Abstract

The network of interpersonal connections is one of the possible heterogeneous factors which affect the income distribution emerging from micro-to-macro economic models. In this paper we equip our model discussed in [1, 2] with a network structure. The model is based on a system of n differential equations of the kinetic discretized-Boltzmann kind. The network structure is incorporated in a probabilistic way, through the introduction of a link density P(α) and of correlation coefficients P(β|α), which give the conditioned probability that an individual with α links is connected to one with β links. We study the properties of the equations and give analytical results concerning the existence, normalization and positivity of the solutions. For a fixed network with P(α) = c/α^q, we investigate numerically the dependence of the detailed and marginal equilibrium distributions on the initial conditions and on the exponent q. Our results are compatible with those obtained from the Bouchaud-Mezard model and from agent-based simulations, and provide additional information about the dependence of the individual income on the level of connectivity.