When a mind develops, it goes through numerous stages of awareness, such as (not necessarily in order)
What do you call the awareness of other's awareness of you (and the logical deduction of what they believe you're thinking)?
I believe this should be the stage before meta-gaming is possible.
This sort of thinking is called theory of mind (not to be confused with theories of how the mind works).
It's not entirely clear whether theory of mind is a discrete ability or a spectrum, but tasks requiring higher-order theorizing tend to be more difficult and are more likely to be lost to dysfunction:
Cognitive theory of mind is further separated into first order (e.g., I think she thinks that…) and second order (e.g., he thinks that she thinks that…)
I'm not aware of a specific term that distinguishes second-order theory of mind when the second-order person is in fact the first-person rather than a third-person (e.g., "she thinks that I think that...").
