"Evolution of Money Distribution in a Simple Economic Model"
An analytical approach is utilized to study the money evolution in a simple agent-based economic model, where every agent randomly selects someone else and gives the target one dollar until he runs out of money. (No one is allowed to go in debt.) If originally no agent is in poverty, for most of time the economy is found to be dominated by a Gaussian money distribution, with a fixed mean and an increasing variance proportional to time. This structure begins to be drifted toward the left when the tail of the Gaussian hits the left boundary, and the drift becomes faster and faster, until a steady state is reached. The steady state generally follows the Boltzmann-Gibbs distribution, except for the points around the origin. Our result shows that, the pdf at the origin is half of that predicted by the Boltzmann solution. An implication of this is that the economic structure may be improved through manipulating market rules.