Differential Equations in Games?

Centuries ago there was a hammurabi game. The basic idea was that you ruled a country. You had to allocate money to buy grain and allocate grain to feed people. You had to tax people to get money. Overtaxed or underfed populations would rebel. There were various causes of crop failure, etc. It seems to me that this is just a set of interacting differential equations. I have long thought that it would be interesting to build a "game construction kit", choosing a set of differential equations (and equating them with game features). Truly difficult cases would include 3-body interactions, etc. Does anyone know of such an approach?