confused. please help.

Question 2. (19 points) Two countries A and B are on the verge of starting immunization population with a Covid-19 vaccine. Each country has two possible actions: immunize (1) and wait (W). The reason for waiting is that the quality of the vaccine is still uncertain - it can be good (efficient, no side effects) or bad (inefficient, cause serious side effects). Assume that the countries plan to use the same vaccine, so it is either efficient or inefficient in any country that uses the vaccine. If the vaccine is good the countries' strategies and payoff matrix are given by the following table: B W A W 1,1 2, 3 1 3, 2 4, 4 The strategic form of the game reflects the fact that immunization started by one country positively affects the other country - say, less immunized travelers will spread the virus in the other country. The maximal benefit is achieved when both countries immunize. If the new vaccine is bad the countries' strategies and payoff matrix are given by the following table:B W 1 A W 1,1 2,4 I -1,2 2,2 The strategic form of the game reects the fact that if the vaccine is bad, the country that used it experiences a loss. If the other country waits, it benets from the knowledge about the vaccine quality. The worst outcome is immunizing the population in both countries with the bad vaccine. Countries A and B choose their actions simultaneously. (a) Describe all (if any) pure strategies Nash equilibria in the case when the vaccine is good. (b) Describe all (if any) pure strategies Nash equilibria in the case when the vaccine is bad. (c) Suppose that the quality of the vaccine is not known. Let 7r 6 (0, 1) denote the probability of the event that the vaccine is good. Write down the strategic form of the game for this case and analyze how pure strategies Nash equilibria depend on the value of 7r. (d) Let 7r = 0.6. If the countries are allowed to randomize their behav- ior, what will be the equilibrium strategies and payoffs