A Random Distribution of Wealth

What happens, if 100 persons in a room are given $100 each and give away a Dollar to one randomly chosen person in this room each tick of the clock? How is wealth distributed over time by pure chance?

While the naïve assumption may suggest an equal distribution of wealth, we typically encounter an exponential curve in the distribution, with a few stable big players. Mind that this "natural" inequality does not include any economic effects, like chances of participations, chances of profitting by a surplus collected each round by a growing economy, or debt, or, on the other hand, effects of any counteracting measures, like proportional taxes, taxation of propetry, or proactive supports.

Here, we simulate a population of 55 players, given a starting capital of $45 each, for 5,000 rounds. (While the general effect will be the same, the slope/gradient of the distribution will be typically flatter for a higher starting capital and/or a bigger population.)

The "Run" button starts a new simulation, which may stopped and resumed any time. Once stopped, you may navigate the entire timeline by means of the slider at the bottom of visualization. Orange bars represent the individual players and their respective wealth, while the blue bars represent the distribution in the population, ordered from the poorest players at the left to the richest one at the far right. The median of this distribution is marked by a dotted line.

(We may observe that the one property mostly preserved by the random distribution process is the median, which will typically stay close in value to the capital distributed initally to the individual players, but will generally show a tendency to decrease with higher iterations.)

Explore!

See also the enhanced model of this simulation.