In this case, game theory says that if both people are using the same logic and they know that, then what I showed above is correct

and

Is it ever the case in reality?

It seems so, yes. We don't have absolutely certain frameworks, but we do have contracts that are enforceable by law, and we have strong trust-based networks.

It is worth pointing out that even in fairly sloppy situations, we can still use "if both people are using the same logic and they know that" rule of thumb. For example, I would never decide to carpool if I though that I could not trust the other person to be on time (but I might frequently be late if there was no cost to doing so). When all members of the carpool make this calculation, even a limited amount of evidence that we all agree that that this calculation makes it worth showing up on time is likely to keep the carpool going; that is, if it works well for two days and on the third day Bob shows up late but has a good excuse and is apologetic, we will probably be willing to pick Bob up on the fourth day.

[Edits; I have no clue how to separate two blocks of quoted text.] [Edit: figured it out].