Consider a game with two players, 1 and 2. They play the extensive-form game summarized in the

Question:

Consider a game with two players, 1 and 2. They play the extensive-form game summarized in the game tree below:

a. Suppose Player 1 is choosing between the gray and black for his second move. Which will he choose if:
i. Gray, Gray has been played.
ii. Black, Black has been played
b. Suppose Player 2 is choosing between green and red, knowing the information above. Which will he choose if:
i. Gray has been played.
ii. Black has been played.
c. Finally, suppose Player 1 is choosing between gray and red in the first move. Given the information above, which will he choose?
d. Now describe the path that gives an equilibrium in this extensive game.