Consider the following sequential game. Wally first chooses L or H. Having observed Wally’s choice, Elizabeth chooses between A and F. The payoffs are as follows. If Wally chose L and Elizabeth chose A, the payoffs are 30 to Wally and 20 to Elizabeth. If Wally chose L and Elizabeth F, the payoffs are 40 to Wally and 10 and to Elizabeth. If Wally decides to opt for H and Elizabeth A, the payoffs are 10 and 2 to Wally and Elizabeth, respectively. Finally, if Wally opts for H and Elizabeth F, the payoffs are 35 toWally and 5 to Elizabeth. What is the outcome in the subgame perfect equilibrium of this game?Group of answer choices(L,F)(H,A)(H,F) and (L,F)(L,A) and (H,F)(H,F)
Question
Consider the following sequential game. Wally first chooses L or H. Having observed Wally’s choice, Elizabeth chooses between A and F. The payoffs are as follows. If Wally chose L and Elizabeth chose A, the payoffs are 30 to Wally and 20 to Elizabeth. If Wally chose L and Elizabeth F, the payoffs are 40 to Wally and 10 and to Elizabeth. If Wally decides to opt for H and Elizabeth A, the payoffs are 10 and 2 to Wally and Elizabeth, respectively. Finally, if Wally opts for H and Elizabeth F, the payoffs are 35 toWally and 5 to Elizabeth. What is the outcome in the subgame perfect equilibrium of this game?Group of answer choices(L,F)(H,A)(H,F) and (L,F)(L,A) and (H,F)(H,F)
Solution
The subgame perfect equilibrium of this game is (L,F) and (H,F).
Here's the step-by-step reasoning:
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First, consider Elizabeth's choices after Wally's move. If Wally chooses L, Elizabeth gets 20 if she chooses A and 10 if she chooses F. So, she prefers A to F after L. If Wally chooses H, Elizabeth gets 2 if she chooses A and 5 if she chooses F. So, she prefers F to A after H.
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Now, consider Wally's choices. If he believes that Elizabeth will follow the strategy we just described, he gets 30 if he chooses L (because Elizabeth will choose A) and 35 if he chooses H (because Elizabeth will choose F). So, he prefers H to L.
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However, if Wally chooses L, knowing that Elizabeth will choose F (because it gives her a higher payoff than A), he gets 40. So, he might want to deviate from H to L.
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Therefore, the subgame perfect equilibrium strategies are (L,F) for the subgame starting at L and (H,F) for the subgame starting at H.
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