1. Prove or disprove: If it is common belief among the players at the state of the world ω that the state of the world is consistent, then Y˜i(ω) =Y˜j (ω) for every pair of players i, j ∈ N.
2. Find an example of a belief space where the set of players consists of two players, and there exists an inconsistent state of the world ω at which πi({ω} | ω) = 0, and each player i believes that the state of the world is inconsistent.