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Follow the Money

Brian Hayes

Crime Doesn't Pay

The two models described so far lie at opposite poles along an axis defined by the amounts the trading parties put at risk. In the yard-sale model, the most that can be won or lost is the total wealth of the poorer partner. Since this model evolves toward a state where nearly everyone is impoverished, the typical transaction is extremely small. In the marriage-divorce model, in contrast, the entire fortunes of both partners are up for grabs.

Here is a recipe for a third model that occupies a middle ground. As in the yard-sale algorithm, pick two trading partners at random, and also randomly choose which of the partners is to lose (the donor) and which is to gain (the recipient). But instead of setting the size of the trade as a random fraction of the poorer player's wealth, make it a random fraction of the wealth of the donor. This rule still satisfies the commonsense constraint that you can never be made to pay more than you have. In each transaction you risk losing a random fraction of your own wealth, but you have a chance to gain a random fraction of the other person's fortune.

What kinds of real-world transactions might be described by this model? No doubt there are many plausible interpretations, but here is one that I find intriguing. A distinctive characteristic of the trading scheme is that the richer party always has more to lose and the poorer more to gain. Under these terms , any sensible person would try to do business only with wealthier partners, and no one would ever willingly choose to trade with a less-affluent person (assuming traders can gauge the wealth of their partners). Thus if trading between nonequals takes place at all, it must be by coercion or deception. In other words, what is being modeled here is theft and fraud.

When the theft-and-fraud model is allowed to run for many iterations, there is no economic collapse. The wealth distribution reaches an equilibrium on an exponential curve much like that seen in the marriage-and-divorce model. (I have no comment on this evidence that marriage and divorce have the same economic impact as larceny, nor will I speculate on why a world populated by bank robbers winds up with a fairer distribution of wealth than an economy of honest merchants.)

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