A Scientific American article explains how simple fair transactions between equal economic agents lead to an inexorably concentrated wealth, resulting in oligarchy,

Simulate the distribution of wealth between agents after a large number of transactions have been done, using the yard sale model:

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What is going on here? Read the Scientific American article on which the simulation is based and look at the source code of this page. Another article Kinetics of wealth and the Pareto law explains math and contains illustrative figures.

The following is a selection of relevant paragraphs from the Scientific American article:

To understand how this happens, suppose you are in a casino and are invited to play a game. You must place some ante—say, $100—on a table, and a fair coin will be flipped. If the coin comes up heads, the house will pay you 20 percent of what you have on the table, resulting in $120 on the table. If the coin comes up tails, the house will take 17 percent of what you have on the table, resulting in $83 left on the table. You can keep your money on the table for as many flips of the coin as you would like (without ever adding to or subtracting from it). Each time you play, you will win 20 percent of what is on the table if the coin comes up heads, and you will lose 17 percent of it if the coin comes up tails. Should you agree to play this game?

With a bit more work you can confirm that it would take about 93 wins to compensate for 91 losses. From this perspective it seems disadvantageous to play this game.

Let each begin with some initial wealth, which could be exactly equal. Choose two agents at random and have them transact, then do the same with another two, and so on. In other words, this model assumes sequential transactions between randomly chosen pairs of agents.

What should a single transaction between a pair of agents look like? People have a natural aversion to going broke, so we assume that the amount at stake, which we call Δω (Δω is pronounced “delta w”), is a mere fraction of the wealth of the poorer person, Shauna. That way, even if Shauna loses in a transaction with Eric, the richer person, the amount she loses is always less than her own total wealth. This is not an unreasonable assumption and in fact captures a self-imposed limitation that most people instinctively observe in their economic life. To begin with—just because these numbers are familiar to us—let us suppose Δω is 20 percent of Shauna's wealth, ω, if she wins and –17 percent of ω if she loses. (Our actual model assumes that the win and loss percentages are equal, but the general outcome still holds. Moreover, increasing or decreasing Δω will just extend the time scale so that more transactions will be required before we can see the ultimate result, which will remain unaltered.)

If you simulate this economy, a variant of the yard sale model, you will get a remarkable result: after a large number of transactions, one agent ends up as an “oligarch” holding practically all the wealth of the economy, and the other 999 end up with virtually nothing.

Author of this simulation: tanel.tammet@gmail.com