Follow the Money
The rich get richer and the poor get poorer. You've heard that before. It is a maxim so often repeated, and so often confirmed by experience, that it begins to sound like a law of nature, as familiar and irresistible as gravity. And indeed perhaps there is some physical or mathematical rule governing the distribution of wealth in the world. No such general principle is going explain the specifics of who gets rich and poor, but it might illuminate the overall statistics.
This idea goes back at least a century to the work of the Italian economist Vilfredo Pareto, who tried to show that the income distribution in all cultures and countries has the same mathematical form. In recent years the topic has been taken up with renewed enthusiasm by a small band of "econophysicists," who apply principles of statistical mechanics to questions in economic theory. The essence of their approach is to study an economy as if it were a many-body physical system such as a gas. Just as random collisions between gas molecules give rise to macroscopic properties such as temperature and pressure, random encounters between individuals in an economic system might determine large-scale phenomena such as the distribution of wealth.
Some of the computational models for exploring these issues are remarkably easy to build and run. It takes just a few minutes' effort and a few lines of code. On the other hand, it's also remarkably easy to make subtle mistakes of implementation, as I'll have occasion to mention below. And the big challenge is not building the models but interpreting the results—deciding which kinds of random encounters might represent events in a real economy.