Assignment:
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},{2, 5},{3},{4, 7},{6, 9},{8}}. What are the connected components in the graph corresponding to this Aumann model? Which events are common knowledge in state of the world ω = 1? Which events are common knowledge in state of the world ω = 9? Which events are common knowledge in state of the world ω = 5?
Provide complete and step by step solution for the question and show calculations and use formulas.