  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.
