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 can make a credible commitment to choosing either Up or Down at B or C, then the subgame rooted at A becomes a sequential game of perfect information. In this subgame, Player 2 has the last move and can choose Down at B or C to maximize his or her payoff.

If Player 2 commits to choosing Up, then Player 1 would choose Down at A to get a payoff of 3, which is better than 2. This would make Player 2 worse off than if he or she had chosen Down as well.

Therefore, Player 2 would not commit to choosing Up.

If Player 2 commits to mimicking Player 1's strategy, then he or she would choose Up at B or C if Player 1 chose Up at A, and Down at B or C if Player 1 chose Down at A. This would result in a payoff of 2 for Player 2 in either case, which is worse than the payoff of 3 for choosing Down at B or C.

Therefore, Player 2 would not commit to mimicking Player 1's strategy.

Therefore, the best choice for Player 2 is to commit to choosing Down at B or C.

Player 1 and Player 2 Are Playing a Game in Which