Consider the following game between players 1 and 2. First, player 1 chooses either In or...

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Consider the following game between players 1 and 2. First, player 1 chooses either In or Out. If Out is chosen, the game ends; player 1 gets payoff of 2 and player 2 gets 1. If In is chosen, then players simultaneously choose either A or B. If both choose A, then player 1 gets payoff of 3 and player 2 gets 1. If both choose B, then 1 gets payoff of 1 and player 2 gets 3. Otherwise (i.e., if their choices are different), then they get payoff of 0. give a proof/defense of your answer on your own paper. (You need to give enough but concise explanation so it should not exceed 2 pages.) a) First, draw a game tree completely to describe this game in an extensive form. Then, make a payoff table to convert it into a strategic form. b) Find all the pure strategy Nash equilibria of this game. To defend your answer, mark the best responses on the payoff table. c) Find all the mixed strategy Nash equilibria of this game. d) A subgame that is not the entire game is called a proper subgame. Find a proper subgame of this game and make a payoff table to describe it in a strategic form. Then, find all the (both pure and mixed strategy) Nash equilibria of this subgame. e) Find all the pure strategy subgame perfect Nash equilibria of this (entire) game. Is there any pure strategy Nash equilib- rium that is not subgame perfect? f) Find all the mixed strategy subgame perfect Nash equilibria of this (entire) game. Consider the following game between players 1 and 2. First, player 1 chooses either In or Out. If Out is chosen, the game ends; player 1 gets payoff of 2 and player 2 gets 1. If In is chosen, then players simultaneously choose either A or B. If both choose A, then player 1 gets payoff of 3 and player 2 gets 1. If both choose B, then 1 gets payoff of 1 and player 2 gets 3. Otherwise (i.e., if their choices are different), then they get payoff of 0. give a proof/defense of your answer on your own paper. (You need to give enough but concise explanation so it should not exceed 2 pages.) a) First, draw a game tree completely to describe this game in an extensive form. Then, make a payoff table to convert it into a strategic form. b) Find all the pure strategy Nash equilibria of this game. To defend your answer, mark the best responses on the payoff table. c) Find all the mixed strategy Nash equilibria of this game. d) A subgame that is not the entire game is called a proper subgame. Find a proper subgame of this game and make a payoff table to describe it in a strategic form. Then, find all the (both pure and mixed strategy) Nash equilibria of this subgame. e) Find all the pure strategy subgame perfect Nash equilibria of this (entire) game. Is there any pure strategy Nash equilib- rium that is not subgame perfect? f) Find all the mixed strategy subgame perfect Nash equilibria of this (entire) game.