Dynamics of Social Diversity
  We introduce and solve analytically a model for the development of disparate social classes in a competitive population. Individuals advance their fitness by competing against those in lower classes, and in parallel, individuals decline due to inactivity. We find a phase transition from a homogeneous, single-class society to a hierarchical, multi-class society. In the latter case, a finite fraction of the population still belongs to the lower class, and the rest of the population is in the middle class, on top of which lies a tiny upper class. While the lower class is static and poor, the middle class is upwardly mobile. 
E. Ben-Naim, S. Redner