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 meanfield 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.