Here is a minor point:

"for all possible sets of observations, each agent knows what the other agent will infer."

This is true if both agents are rational (and this is common knowledge) and share a common prior (and this is common knowledge). You can calculate what they would infer using Bayesian math.

If you are unsure about someone's ability to observe data about the real world, then that's another fact about the real world that you can have beliefs about. You shouldn't have to talk endlessly about everything.