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. If Player 2 could make a credible commitment to choose either Up or Down when his or her turn came, then what would Player 2 do?
A)Player 2 would not commit to choosing either strategy.
B)Player 2 would commit to choosing Up.
C)Player 2 would commit to choosing Down.
D)Player 2 would commit to mimicking Player 1's strategy.

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.  If Player 2 could make a credible commitment to choose either Up or Down when his or her turn came, then what would Player 2 do?
A)Player 2 would not commit to choosing either strategy. 
B)Player 2 would commit to choosing Up. 
C)Player 2 would commit to choosing Down. 
D)Player 2 would commit to mimicking Player 1's strategy.

Quizplus · Accepted Answer

If Player 2 commits to choosing Down, then Player 1 will pick Up, and Player 2's payoff will be $40. If Player 2 commits to playing Up, then Player 1 will pick Down, and Player 2's payoff will be $11, and if Player 2 commits to mimicking Player 1's strategy, then Player 1 will choose Down, and Player 2's payoff will be $10. Thus, Player 2's payoff is the highest when Player 2 commits to choosing Down.

Player 1 and Player 2 Are Playing a Game in Which