Coming from a background in scientific instruments, I always find this kind of analysis a bit jarring with its infinite regress involving the rational, self-interested actor at the core.

Of course two instruments will agree if they share the same nature, within the same environment, measuring the same object. You can map onto that a model of priors, likelihood function and observed evidence if you wish. Translated to agreement between two agents, the only thing remaining is an effective model of the relationship of the observer to the observed.