How the rich get richer
  In our model, $n$ traders interact with each other and with a central bank; they are taxed on the money they make, some of which is dissipated away by corruption. A generic feature of our model is that the richest trader always wins by 'consuming' all the others: another is the existence of a threshold wealth, below which all traders go bankrupt. The two-trader case is examined in detail,in the socialist and capitalist limits, which generalise easily to $n>2$. In its mean-field incarnation, our model exhibits a two-time-scale glassy dynamics, as well as an astonishing universality.When preference is given to local interactions in finite neighbourhoods,a novel feature emerges: instead of at most one overall winner in the system,finite numbers of winners emerge, each one the overlord of a particular region.The patterns formed by such winners (metastable states) are very much a consequence of initial conditions, so that the fate of the marketplace is ruled by its past history; hysteresis is thus also manifested. 
Anita Mehta, A. S. Majumdar and J. M. Luck