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Question: 8 common knowledge 12 points i 8 points prove the...

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8. COMMON KNOWLEDGE (12 POINTS) I. (8 points) Prove the Lemma from the notes, that an event E is self-evident if and only if E is the union of elements of each players information partition. (Hint: h) is an element of the players information partition, by definition) 2. (4 points) Provide an example of a non-partitional information function where it is common knowledge that agents disagree about the value of a random variable (i.e., a function that depends on the state of the world θ), and use it to construct an example of favorable trade. Hint:You can construct an example with three states where one player receives no information.
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