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 played 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 found 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.