This scenario does not satisfy the premises for Aumann’s Agreement Theorem. There is no common knowledge since in almost all observations by Alice, Bob is dead and in no state to have common knowledge with Alice of anything at all. Even without invoking quantum suicide and anthropic conditionals, the second simple coin-toss example in Aumann’s original paper shows a case where the participants do not have common knowledge and hence do not necessarily agree on posterior probabilities.
This scenario does not satisfy the premises for Aumann’s Agreement Theorem. There is no common knowledge since in almost all observations by Alice, Bob is dead and in no state to have common knowledge with Alice of anything at all. Even without invoking quantum suicide and anthropic conditionals, the second simple coin-toss example in Aumann’s original paper shows a case where the participants do not have common knowledge and hence do not necessarily agree on posterior probabilities.
In the one world.where they both survive, do they satisfy the premises?