I like the examples of quickly-resolved disagreements.
They don’t seem that Aumannian to me. They are situations where one person’s information is a subset of the other person’s information, and they can be quickly resolved by having the less-informed person adopt the belief of the more-informed person. That’s a special case of Aumann situations which is much easier to resolve in practice than the general case.
Aumann-in-general involves reaching agreement even between people who have different pieces of relevant information, where the shared posterior after the conversation is different from either person’s belief at the start of the conversation. The challenge is: can they use all the information they have to reach the best possible belief, when that information is spread across multiple people? That’s much less of a challenge when one person starts out with the full combined set of information.
(Note: my understanding of Aumann’s theorem is mostly secondhand, from posts like this and this.)
This is pretty common in any joint planning exercise. My friend and I are deciding which movie to see together. We share relevant information about what movies are available and what movies we each like and what movies we have seen. We both conclude that this movie here is the best one to see together.
I like the examples of quickly-resolved disagreements.
They don’t seem that Aumannian to me. They are situations where one person’s information is a subset of the other person’s information, and they can be quickly resolved by having the less-informed person adopt the belief of the more-informed person. That’s a special case of Aumann situations which is much easier to resolve in practice than the general case.
Aumann-in-general involves reaching agreement even between people who have different pieces of relevant information, where the shared posterior after the conversation is different from either person’s belief at the start of the conversation. The challenge is: can they use all the information they have to reach the best possible belief, when that information is spread across multiple people? That’s much less of a challenge when one person starts out with the full combined set of information.
(Note: my understanding of Aumann’s theorem is mostly secondhand, from posts like this and this.)
This is pretty common in any joint planning exercise. My friend and I are deciding which movie to see together. We share relevant information about what movies are available and what movies we each like and what movies we have seen. We both conclude that this movie here is the best one to see together.