What if for A to cheat means that you necessarily just mistaken about which algorithm A runs?

A decision algorithm should never be mistaken, only uncertain.

UDT will be logically certain about some things but not others. If UDT B "doesn't update" on its computation about what A will do in response to B, it's going to be in trouble.

"Doesn't update" doesn't mean that it doesn't use the info (but you know that, so what do you mean?). A logical conclusion can be a parameter in a strategy, without making the algorithm unable to reason about what it would be like if the conclusion was different, that is basically about uncertainty of same algorithm in other states of knowledge.