6. Consider the game, \"The Battle of the Bismarck Sea.\" The game depicts a real life example where, in March 1943, the Commander of the US Fleet had to determine where to send his planes around the Island of New Britain to engage the Japanese convoy. Suppose the US has the choice of sending its planes North, or South. Likewise, Japan can choose the strategies North and South, reflecting the position of its ships. The payoffs as shown in the matrix below: JAPAN MNorth South UNITED STATES The positive numbers reflect "days of bombing,\" which are a positive payoff for the United States but negative payoff to the Japanese. Using pure strategies: a. What is the best response function of the United States and Japan? Write these out in words and then show them in the game matrix itself. b. Find any Nash Equilibria. Now suppose that when the US runs North, and Japan runs South, rather than get partly intercepted, the US completely misses the target and gets no days of bombing. The payoffs become: MNorth South UNITED STATES c. Find any Nash equilibria. Comment on your answer. d. Is this a Prisoner's Dilemma-type game? Explain