Consider an Aumann model of incomplete information in which N = {I, II}, Y = {1, 2, 3, 4, 5, 6, 7, 8, 9}, FI = {{1, 2, 3},{4, 5, 6},{7, 8, 9}}, and FII = {{1, 5},{2, 6},{3, 4},{7},{8, 9}}. Answer the following questions:
(a) What are the connected components in the graph corresponding to the Aumann model?
(b) Which events are common knowledge in state of the world ω = 1? In ω = 7? In ω = 8?
(c) Denote by A the event {1, 2, 3, 4, 5}. Find the shortest sequence of players i1, i2,...,ik such that in the state of the world ω = 1 it is not the case that i1 knows that i2 knows that ...ik-1 knows that ik knows event A.