Problem
Suppose you have the following game, which describes the conflict in the Southeast Asian sea during World War II.
The game depicts a real life example where the Commander of the US Fleet, General Kenney, had to determine whether to send his planes to the North or South around the Island of New Britain to engage the Japanese convoy.
The payoffs as shown in the matrix below:
|
|
JAPAN
|
|
UNITED STATES
|
|
North
|
South
|
|
North
|
2, - 2
|
2, - 2
|
|
South
|
1, - 1
|
3, - 3
|
The positive numbers reflect "days of bombing," which are a positive payoff for the United States but negative payoff to the Japanese.
(a) What is the best response function of the United States and Japan? Write these out in words and then show them (clearly) in the game matrix itself.
(b) Find any Nash Equilibria using the pure strategies North and South. Explain.
(c) Is this game characterized by dominant strategies? Explain.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.