# A Random Distribution of Wealth (3)

Simulation:

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?

Here, we simulate a population of 55 players, given a starting capital of \$45 each, for 5,000 rounds.

This model is the same as in the basic version, but includes basic economics, like debt (whithout interest) and investments that are geometrically proportional to the respective wealths of the spending and the receiving player (but may not undercut a liminal cost of a quarter Dollar per round).
As compared to the model using linear proportional transactions, we here see another, rather dramating increase in inequality. — Mind the doubled scale of the y-axis!

So for any transactions between two players (Pi : Pr)t wealths W are mutated by a turnover z as in

Wi,t = Wi, t-1z

and

Wr,t = Wr, t-1 + z

where

z = √( (Wi, t-1 ÷ Wt0)2 + (Wr, t-1 ÷ Wt0)2 ) and z ≥ 0.25

Thus, z will be 1 at t1 and growth rates will evolve in subsequent iterations with the developing market positions of the individual players involved in a transaction.

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.

See also the enhanced version of this model, resulting in a norrower, Gaussian distribution and stable median value by limiting expenses to available capitial.

Explore!

℗ 2017 www.masswerk.at, based on an article in Decision Science News.