Is there a simplified mathematical model that allows accurate premonitions?

That is, a model where:

- The world consists of deterministic agents, each with some goal, making decisions based on available information to optimize for that goal.

- There is an initial state, such that, if you give some (or all) of the agents some information about a future state (or even a complete description of it), then the world is guaranteed to evolve into a future state consistent with that information.

I'm sure it's straightforward to give trivial models (e.g., any model where the future is fixed), so the question is how general we can make the model.