The game known as the Battle of the Bismarck Sea (named for that part of the south-western Pacific Ocean separating the Bismarck Archipelago from Papua-New Guinea) summarizes a well-known game actually played in 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 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 fund the Japanese right away but only one day of bombing if they found that the Japanese had gone north.
a) Illustrate this game in a game table.
b) Identify any dominant strategies in the game and solve for the Nash equilibrium.
c) Apply the min-max method to solve this game.
d) Discuss the characteristics of this game by categorizing it according to the six dimensions outlined in the lecture or in the textbook.