  We mathematically analyze a simple market model where trading at each point
in time involves only two agents with the sum of their money being conserved
and with neither parties resulting with negative money after the interaction
process. The exchange involves random re-distribution among the two players of
a fixed fraction of their total money. We obtain a simple integral nonlinear
equation for the money distribution. We find that the zero savings and finite
savings cases belong to different universality classes. While the zero savings
case can be solved analytically, the finite savings solution is obtained by
numerically solving the integral equation. We find remarkable agreement with
results obtained by other researchers using sophisticated numerical techniques.
