Bayes-Nash Equilibrium

5. Suppose there are two firms and one market. Both firms choose whether to invest and adapt a technology or not. However, Firm A can be one of two possible types, either high or low cost with the associated probabilities @ and 1-0. Firm A observes its own type but B cannot observe A's. The normal form version of this game presented below, given the two possible states of nature. Firm B Don't Firm B Don't Invest Invest Invest Invest Firm A Firm A Invest 6, 1 3,0 Invest 3, 1 0, 0 Don't Don't Invest 0, 0 1, 3 Invest 0, 0 1, 3 A High Cost: 0 A Low Cost: 1-0 Allowing for mixed strategies, let (q, 1-q) represent the probabilities that Firm B invests and doesn't invest and and let (p , 1-pa) be the probabilities that Firm A invests and doesn't invest if it is a high cost type and let (Pz, 1-pz) be the probabilities that A will invest or not if it is a low cost type. 5.a) Find the set of best responses for the privately informed player, Firm A , and then find the best response of the uninformed player as a function of 0. 5.b) Find the Bayes-Nash Equilibria of the above game when 0 =2/3