the definition for simulation on the Internet is:
[sɪmjuːˈleɪʃ(ə)n]
NOUN
imitation of a situation or process:
"simulation of blood flowing through arteries and veins" ·
the action of pretending; deception: (like faking orgasm my note)
Simulation is basically an illusion. We often think about something that`s about to happen, it`s something we do every day. However the next level in thinking about something that`s about to happen is to create a material support/prove/aid for the thing that is about to happen that is not the thing itself. Astronauts do this very often, they create 1:1 copies of environment they will face in the future, and perform the operations on the copy. Another more common example of simulations are military drills. Basically the simulations allow us to ‘travel into the future’ and Spot problems.
I think you're so focused on the idea of mental models, so that you forget about actual reality.
For a game that means: You need simulation first and foremost to simulate the actual reality of the game. E.g. Characters walking over terrain and not falling through, inability to walk or shoot through doors, maybe even rigid bodies, ragdolls, vehicles, etc.
In this context, the simulation is no illusion but models reality. Ignoring the point of it being a fictional reality.
And because reality is more essential than intelligence to get a game, you might want to work on the former first.
After that, you see how much of it can be reused to run mental simulations, or if a simplified system is needed.
The problem is: you have to work on the problems you actually have right now, not the problems which are interesting.
If you don't like that, do what i did: Quit working on a game, and focus entirely in research of crazy ideas.
But be warned: I really miss to produce something… playable ; )