Since I brought up the topic, a commenter pointed me to the Wikipedia article on complexity in economics, and that in turn referred to David Colander.

[complexity theory] is highly mathematical, and, as I stated above, accepts the need for simplification. But it argues that the mathematics needed to simplify economics often involves non-linear dynamic models that have no deterministic solution.

He concludes,

The methodology of complexity economics is quite consistent with the methodology of standard economics and, as such, does not fit well with many heterodox traditions. Still, many heterodox economists have had a complexity vision, and thus complexity economics can be seen as a melding of heterodox vision with standard scientific methods, which is only now coming of age.

It strikes me that there is a deep question of what constitutes knowledge in economics. I do not know the answer, but my instinct is that the contribution of computer simulations of complex processes will not amount to much.