Reference no: EM132151929

Game Theory Assignment -

Question 1 - Consider the same informational cascade game as in Lecture 10 (prior belief = 0.5, payoff of correct choice = 1, payoff of wrong choice = 0). Let the signal accuracy be 0.9 for every player: P(sL|L) = P(sR|R) = 0.9.

If the first consumer chooses L, what is his posterior belief P(L) at the time of his choice?

Question 2 - If the first player chooses L and the second player chooses R, what is the second player's posterior belief P(L) at the time of his choice?

Question 3 - Consider the same informational cascade game as in Lecture 10 (prior belief = 0.5, payoff of correct choice = 1, payoff of wrong choice = 0). Assume that when players are indifferent, they flip a fair coin.

Suppose the accuracy of the first player's signal is 0.9 and the accuracy of all later players' signals is 0.7. What is the unconditional probability of having the following choice sequence?

L L L L L L L (all players choose L)

Question 4 - Suppose the accuracy of the first player's signal is 0.9 and the accuracy of all later players' signals is 0.7. What is the conditional probability of having the following choice sequence when, in fact, L is the better choice?

R R R R R R (all players choose R)

Note - Please write your answer in digits, not fraction.