Question 1 Consider the following simultaneous-move game. X Player 1 Y Player 2 A B C 2,5 7,1 5,7 3,6 6,7 9, 10 8,2 5,3

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Question 1 Consider The Following Simultaneous Move Game X Player 1 Y Player 2 A B C 2 5 7 1 5 7 3 6 6 7 9 10 8 2 5 3 1 (69.73 KiB) Viewed 6 times

Question 1 Consider the following simultaneous-move game. X Player 1 Y Player 2 A B C 2,5 7,1 5,7 3,6 6,7 9, 10 8,2 5,3 Z 3,3 (a) (1 point) Find all Nash equilibria in pure strategies. Suppose now the game is played sequentially. First, player 1 chooses an action. Then, player 2 observes player 1's move, and chooses an action. (b) (2 points) Draw the extensive-form game. How many pure strategies does each player have? (c) (2 points) Find all subgame-perfect Nash equilibria of the sequential game. Suppose, as in the beginning, the game is played simultaneously. However, now, players play the game twice in a row and observe each other's first-stage action before choosing actions in the second stage. Both players discount second-stage payoffs using a common discount factor & € [0, 1]. (d) (2 points) How many pure strategies does each player have in the two-stage game? (e) (3 points) What is the smallest & for which profile (Y, B) can be played in the first stage of a subgame perfect equilibrium?