Image is below

1. (42 points, 7 points per subquestion) A professor is deciding whether or not to admit a student to a special honours programme. Some students are intellectuals (6 = i) and some students are philistines (6 = p). The professor gets a utility of 2 from admitting an intellectual student, a utility of zero from rejecting either type of student, or a utility of 2 from admitting a philistine. The professor cannot observe the student's type, but can observe the activity the student engages in. Students can choose between reading Dostoyevsky (D), or watching reality TV (K). Smart students prefer reading and not-sosmart students prefer watching TV. A student gets a utility of 1 from engaging in her preferred activity, and 1 from engaging in the other activity. A student also gets a utility of 5 from being admitted into the honours class and a utility of 1 from not being admitted. The timing is as follows. First, nature chooses a type for the student. The probability of a student being an intellectual is A = %. After observing the type, the student chooses an activity. The professor observes the activity and decides to admit or not admit the student. A student's total utility is the sum of her utility from the activity and the utility from being admitted or not. a. Draw the extensive form of this game. b. Are there any separating equilibria in which the intellectual type reads Dostoyevsky and the philistine type watches TV? Why (not)? c. Are there any separating equilibria in which the philistine type reads Dostoyevsky'? Why (not)? d. Are there any pooling equilibria with both types choosing to read Dostoyevsky? Why (not)? e. Are there any pooling equilibria with both types watching TV. Why (not)? f. Either explain intuitively or formally invoke the intuitive criterion to argue which of the equilibria you expect to obtain