In Tom Clancy's novel Hunt for Red October, the Soviet Union has developed a submarine named...

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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. The captain initially decides whether or not to send the letter. After revealing his decision to his officers (once they are all out to sea), the officers, which, for the sake of parsimony, are limited to Captain Second Rank Borodin and Lieutenant Melekhin. simultaneously decide between continuing with the plan to defect or reneging on the plan and insisting that the submarine return to the Soviet Union. The payoffs are such that all three players would like to defect and would prefer that it be done without the letter being sent (which results in the Soviet government sending out another submarine to sink Red October).+ FIGURE PR9.5 Hunt for Red October Defect Defect Ramius Borodin Melekhin 7 4 4 Send letter Renege 3 ~ 3 2 Defect 3 3 2 Renege Ramius 1 Renege Defect Defect 8 00 00 8 Do not send lettter 8 Borodin Renege Defect 665 6 5 6 Renege Melekhin Renege 477 A) how many proper subgames are there? B) Show each of these proper subgames in strategic form. C) Find all subgame perfect Nash equilibrium profiles for each proper sub- game. D) Find all subgame perfect Nash equilibrium profiles for the entire game. 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. The captain initially decides whether or not to send the letter. After revealing his decision to his officers (once they are all out to sea), the officers, which, for the sake of parsimony, are limited to Captain Second Rank Borodin and Lieutenant Melekhin. simultaneously decide between continuing with the plan to defect or reneging on the plan and insisting that the submarine return to the Soviet Union. The payoffs are such that all three players would like to defect and would prefer that it be done without the letter being sent (which results in the Soviet government sending out another submarine to sink Red October).+ FIGURE PR9.5 Hunt for Red October Defect Defect Ramius Borodin Melekhin 7 4 4 Send letter Renege 3 ~ 3 2 Defect 3 3 2 Renege Ramius 1 Renege Defect Defect 8 00 00 8 Do not send lettter 8 Borodin Renege Defect 665 6 5 6 Renege Melekhin Renege 477 A) how many proper subgames are there? B) Show each of these proper subgames in strategic form. C) Find all subgame perfect Nash equilibrium profiles for each proper sub- game. D) Find all subgame perfect Nash equilibrium profiles for the entire game.

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A proper subgame is a subset of a game that includes an initial node as well as the Nash equilibrium ... View the full answer