Eur. Phys. J. B 49, 531-538 (2006)
https://doi.org/10.1140/epjb/e2006-00095-y

On the structure of competitive societies

¹ Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
² Department of Physics, Boston University, Boston, Massachusetts, 02215, USA

Corresponding authors: ^a ebn@lanl.gov - ^b fvazquez@buphy.bu.edu - ^c redner@bu.edu

Received: 15 December 2005
Published online: 31 March 2006

Abstract

We model the dynamics of social structure by a simple interacting particle system. The social standing of an individual agent is represented by an integer-valued fitness that changes via two offsetting processes. When two agents interact one advances: the fitter with probability p and the less fit with probability 1-p. The fitness of an agent may also decline with rate r. From a scaling analysis of the underlying master equations for the fitness distribution of the population, we find four distinct social structures as a function of the governing parameters p and r. These include: (i) a static lower-class society where all agents have finite fitness; (ii) an upwardly-mobile middle-class society; (iii) a hierarchical society where a finite fraction of the population belongs to a middle class and a complementary fraction to the lower class; (iv) an egalitarian society where all agents are upwardly mobile and have nearly the same fitness. We determine the basic features of the fitness distributions in these four phases.