This answer is great because it takes the problem with the initial game (one person gets to update and the other doesn’t) and returns the symmetry by allowing both players to update. The end result shows who is better at Aumann updating and should get you closer to the real answer.
If you’d rather know who has the best private beliefs to start with, you can resolve the asymmetry in the other direction and make everyone commit to their numbers before hearing anyone else’s. This adds a slight bit of complexity if you can’t trust the competitors to be honest, but it’s easily solved by either paper/pencil or everyone texting their answer to the person who is going to keep their phone in their pocket and say their answer first.
This answer is great because it takes the problem with the initial game (one person gets to update and the other doesn’t) and returns the symmetry by allowing both players to update. The end result shows who is better at Aumann updating and should get you closer to the real answer.
If you’d rather know who has the best private beliefs to start with, you can resolve the asymmetry in the other direction and make everyone commit to their numbers before hearing anyone else’s. This adds a slight bit of complexity if you can’t trust the competitors to be honest, but it’s easily solved by either paper/pencil or everyone texting their answer to the person who is going to keep their phone in their pocket and say their answer first.