You should provide explanations for all your answers. While you are welcome to use Bayes' formula, you are not required to do so. Consider an information cascade problem with asymmetric signals. There are two states of the world, Y and N, with prior belief that P(Y) = P(N) = 0.5. Ann's utility when she takes action TA in state Y or action 73A in state N is 1; it is 0 otherwise. (a) [3pt] Suppose Ann has not received any signal about the true state of the world and must base her action only on the information given above. What is Ann's optimal action? Explain. Suppose Ann receives signals Em and 11A with probabilities p(yA|Y) : 0.25, p(nA|Y) : 0.75, p(yA|NJ = 0,1)(HAIN) = 1- (b) [3pt] Suppose Ann receives signal 954. What is Ann's optimal action? (c) [3pt] Suppose Ann receives signal 111;. What is Ann's optimal action? Suppose Bob's signals 393, 11.3 are generated according to the following probabilities: P(yB|Y) = P(nB|N) = 0.9, P(nB|Y) = P(yB|N) = 0.1 (d) [3pt] Suppose Bob observes Ann's action and receives signal ya. What is Bob's optimal action? (You need to provide an answer for each possible action of Ann) (e) [3pt] Suppose Bob observes Ann's action and receives signal 713. What is Bob's optimal action? [You need to provide an answer for each possible action of Ann) (f) [6pt] Suppose that Carol, before receiving her own signal, wants to calculate her belief about states Y and N. Calculate Carol's belief for each feasible sequence of actions by Ann and Bob; do not simplify your expressions. Suppose Carol's signals yo, no are generated according to the following probabilities: P(yC|Y) : P(nC|N) : 0.9, P(ng|Y) : P(yC|N) : 0.1. Suppose that it is important for Carol to match the action with the state only when the state is N, but not when the state is Y. That is, Carol's utility is equal to 1 when she takes action no in state N; in all other cases, her utility is 0. (g) [5pt] Identify Carol's optimal actions for every feasible sequence of decisions by Ann and Bob