3. Consider the following two player extensive form game of complete information. In the first stage, player 1 can choose whether to take a hostage or not. If they do not take a hostage, the game ends. If they do take a hostage, player 2 has a choice of whether to pay the ransom or not. Then, player 1 has a choice of whether to continue to hold the hostage or release the hostage, regardless of whether the ransom was paid or not. The game and associated payoffs are provided in the following game tree. (a) Assume x=1 and y=2. What is the unique subgame perfect Nash equilibrium of the game? (b) Assume x=2 and y=1. What is the unique subgame perfect Nash equilibrium of the game? (c) How do the values of x and y affect player 1's decision to take a hostage? According to this simple model, what is something that would lead to fewer hostages being taken? 3. Consider the following two player extensive form game of complete information. In the first stage, player 1 can choose whether to take a hostage or not. If they do not take a hostage, the game ends. If they do take a hostage, player 2 has a choice of whether to pay the ransom or not. Then, player 1 has a choice of whether to continue to hold the hostage or release the hostage, regardless of whether the ransom was paid or not. The game and associated payoffs are provided in the following game tree. (a) Assume x=1 and y=2. What is the unique subgame perfect Nash equilibrium of the game? (b) Assume x=2 and y=1. What is the unique subgame perfect Nash equilibrium of the game? (c) How do the values of x and y affect player 1's decision to take a hostage? According to this simple model, what is something that would lead to fewer hostages being taken