The kibitzer computes the average of these three probabilities and announces the result of his computation publicly. Beatrice and Carol update their probabilities for F in the light of this new information. They then privately report their current posterior probabilities to the kibitzer, who again publicly announces their average, and so on. a. Draw again, but modify it to show the situation after the kibitzers first announcement. b. Repeat (a) for the kibitzers second announcement. c. Repeat (a) for the kibitzers third announcement.

How many announcements are necessary before consensus is reached on the probability of F? e. What will the sequence of events be when the true state of the world is o 1? f. If the true state of the world is o 1, does this ever become common knowledge? g. If o 5 isnt the true state, at which stage will this fact become common knowledge? h. If o is even, at what stage does this become common knowledge? i. Consensus is reached when everybody reports the same probability for F to the kibitzer. Why is it common knowledge that consensus has been reached as soon as it happens?