In Tom Clancy's novel Hunt for Red October, the Soviet Union has developed a submarine named Red October that can run "silently" and thereby escape detection. On its maiden voyage, the ship's captain, Marko Ramius, has decided to defect, because he believes that this technology risks war by destroying the balance of power between the United States and the U.S.S.R. He has put together a set of officers who are loyal to him and have agreed to defect as well. However, the captain is concerned that an officer may change his mind during the voyage and, furthermore, that an officer may be more inclined to change his mind if he thinks that other officers will do so. The captain is then considering writing a letter?to be delivered to the Soviet government after the submarine has departed from its base?stating his plan to defect. The extensive form of this game is shown in FIGURE PR9.5.

A) how many proper subgames are there?

B) Show each of these proper subgames in strategic form

C) Find all subgame perfect Nash equilibrium pro?les for each proper subgame.

D) Find all subgame perfect Nash equilibrium pro?les for the entire game.

FIGURE PR9.5 Hunt for Red October Ramius Send letter Do not send lettter Borodin Defect Renege Defect Renege Melekhin Defect Renege Defect Renege Defect Renege Defect Renege Ramius 3 6 Borodin 2 3 8 6 4 5 7 Melekhin 4 3 N 8 5 6 7