On The Structure of Competitive Societies
E. Ben-Naim, F. Vazquez, and S. Redner
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.
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