Player 1 and Player 2 are playing a game in which Player 1 has the first move at A in the decision tree shown below. Once Player 1 has chosen either Up or Down, Player 2, who can see what Player 1 has chosen, must choose Up or Down at B or C. Both players know the payoffs at the end of each branch. What is the equilibrium outcome of this game?
A)Player 1 and Player 2 both choose Up.
B)Player 1 and Player 2 both choose Down.
C)Player 1 chooses Up and Player 2 chooses Down.
D)Player 1 chooses Down and Player 2 chooses Up.

Question

Player 1 and Player 2 are playing a game in which Player 1 has the first move at A in the decision tree shown below. Once Player 1 has chosen either Up or Down, Player 2, who can see what Player 1 has chosen, must choose Up or Down at B or C. Both players know the payoffs at the end of each branch.  What is the equilibrium outcome of this game?
A)Player 1 and Player 2 both choose Up. 
B)Player 1 and Player 2 both choose Down. 
C)Player 1 chooses Up and Player 2 chooses Down. 
D)Player 1 chooses Down and Player 2 chooses Up.

Quizplus · Accepted Answer

If Player 1 chooses Up, then Player 2 will choose down, so Player 1's payoff will be $30. On the other hand, if Player 1 chooses Down, then Player 2 will choose Up, so Player 1's payoff will be $10. Since $30 is greater than $10, Player 1 will choose Up, and Player 2 will follow by choosing Down.

Player 1 and Player 2 Are Playing a Game in Which