Bayesian agents are logically omniscient, and I think a large fraction of deceptive practices rely on asymmetries in computation time between two agents with access to slightly different information (like generating a lie and checking the consistencies between this new statement and all my previous statements)
My sense is also that two-player games with bayesian agents are actually underspecified and give rise to all kinds of weird things due to the necessity for infinite regress (i.e. an agent modeling the other agent modeling themselves modeling the other agent, etc.), which doesn't actually reliably converge, though I am not confident. A lot of decision-theory seems to do weird things with bayesian agents.
So overall, not sure how well you can prove theorems in this space, without having made a lot of progress in decision-theory, and I expect the resolution to a lot of our confusions in decision-theory to be resolved by moving away from bayesianism.