Let's consider a different problem. There are 100 non-negative numbers summing up to 10000. Let's choose a random combination of numbers satisfying this condition. Intuitively, it's quite clear that typical case will be very different from equilibrium (where every number=100). I fail to see how the transfer of 1 dollar at a time is qualitatively different. So the result is quite intuitive - contrary to what the article suggests.