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3. (40 points) The following questions relate to the Bayesian extensive- form game given on the next page. Nature mom rst, selecting player 1 to be type L with probability 1/4, type M with probability 1/ 4, and type H with probability 1/2, Player 1 observes his type, and either chooses D or N . If player 1 chooses D, the game ends. If player 1 chooses N, player 2 observes player 1's action but not his type, in which case she must choose either B or NB. [The "story" behind this game is that player 1 is a rm, costlessly producing a product that is either low, medium, or high quality, and charging a price of $3. The rm observes its quality and decides whether to disclose it to the consumer (D), or not disclose the quality (N). Then the consumer decides whether to buy or not, Low quality provides a use value of 1, medium quality provides a use value of 2, and high quality provides a use value of 4, so if the quality is disclosed, she would only buy a high quality product] (a) {20 points) Conve'rt this game into Bayesian normal form. (b) (20 points) Denote player 2's beliefs about the thfee types of player 1, conditional on her information set, by (IL, 11'\