4. Complete the payoff table below to represent the choices of the U.S. and Japan in the Battle of the Bismark Sea. Let the U.S. payoffs be days with bombing and the Japanese payoffs be days without bombing, so that the payoffs in each cell have the same sum. The Battle of the Bismarck Sea (named for that part of the southwestern Pacific Ocean separating the Bismarck Archipelago from Papua New Guinea) was a naval engagement between the United States and Japan during World War II. In 1943, a Japanese admiral was ordered to move a convoy of ships to New Guinea; he had to choose between a rainy northern route and a sunnier southern route, both of which required three days' sailing time. The Americans knew that the convoy would. sail and wanted to send bombers after it, but they did not know which route it would take. The Americans had to send reconnaissance planes WOR to scout for the convoy, but they had only enough reconnaissance planes to explore one route at a time. Both the Japanese and the Americans had to make their decisions with no knowledge of the plans being made by the other side. If the convoy was on the route that the Americans explored first, they could send bombers right away; if not, they lost a day of bombing. Poor weather on the northern route would also hamper bombing. If the Americans explored the northern route and found the Japanese right away, they could expect only two (of three) good bombing days; if they explored the northern route and found that the Japanese had gone south, they could also expect two days of bombing. If the Americans chose to explore the southern route first, they could expect three full days of bombing if they found the Japanese right away, but only one day of bombing if they found that the Japanese had gone north. United States North South Japan North 2, South 0 A. Insert the missing payoffs for the U.S. and Japan and do a best response analysis in the payoff table (use circles) B. Identify any dominant strategies (strongly or weakly) for the players. C. Find the Nash (NE) equilibrium (pair of strategies, one for each player, with each being a best response to the strategy of the other player).