3. BNE. You manage a firm developing two types of medicines and sharing the market with another bio firm. Your competitor has labs suitable to produce medicine X, while your firm has labs suitable to produce medicine Y. However, your marketing skill is better to sell medicine X while your competitor's is to medicine Y. If your relationship is tense (unknown probability, could be assumed to be p), you two would agree to share each other's lab, but not collaborating to develop medicines, and sell the products separately. Otherwise (with probability 1 - p, then), you two can develop and sell products collaboratively, and the payoffs would be better than working alone. The detailed payoff matrix showing profits (in million $) can be found below: A: tense relationship (p) Profits Another bio firm X Y (0,4) (2,0) You X (3, 0) Y (0,1) B: nice relationship (1 - p) Profits Another bio firm X Y (4,2) (0, 0) You X Y (0, 0) (3,5) (1) What is your expected payoff when you choose medicine X, and your competitor chooses Y under the tense relationship and chooses X under the nice relationship? (2) Find the Bayes Nash Equilibrium of this question. (3) You are unsure about p, assume that your first hunch is p = 80%, a very tense relationship. But now, the manager in the other bio firm invites you to watch a baseball game together. You know that about 75% under a nice relationship do people invite others to watch game together (P(signal|nice) = 0.75). Use Bayes' Rule to calculate p.