I'm struggling with question 1.4. Can you please explain how to approach it?

ECON2112 Game Theory 85 Business Strategy Problem Set 6 1 Mark and Jason are playing the game depicted in Figure 1. Call 6 = left and H = right the two possible states (or types of M) in the obvious way. That is, Pr (9 = r) = p, with p assumed to be strictly between 0 and 1. They are very shy, so they refused to tell me their payo's, but Jason told me that he would play A only if he thought that M is of type i with probability at least %. For this exercise, you should apply Bayes' rule as you were told to do by your tutors. 1.1 Suppose that everybody knows that M plays the fol- lowing strategy: a if 9 = 1" 9 = ' sl ) {6 its 2 I. J is told that M played bthat is, the information set at which J moves has been reached. What should J believe about 6'? Dene 0(6) 5 Pr(M plays 5 | 3} . That is, a (7') is the probability that M plays 5 ifthe state is r and 0(1) is the probability that 1111 plays 5 if the state is I. Figure 1: Mark and Jason 1.2 Suppose that everybody knows that M plays a strat- egy 0(6) such that 0(3'") 2 0(1) 2 0. J is told that M played bthat is, the information set at which J moves has been reached. What should J believe about 6? 1.3 You are told that J believes that M is more likely to be of type I if he has played I) than if he has played a. What does this imply about 00!") and 00!)? 1.4 You are told that, after using Bayes' rule correctly, J weakly prefers to play A. What does this imply about 0(1\") and 0(1)