This game involves three players, each making sequential decisions. The game proceeds as follows: Player 1 initiates the game by choosing between two actions: Left and Right. • Depending on Player 1's choice, Player 2 then decides, choosing between two actions, left (I) and right (`r`). Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and 'b'.
This game involves three players, each making sequential decisions. The game proceeds as follows: Player 1 initiates the game by choosing between two actions: Left and Right. • Depending on Player 1's choice, Player 2 then decides, choosing between two actions, left (I) and right (`r`). Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and 'b'.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![Consider the following sequential-move game:
This game involves three players, each making sequential decisions. The game proceeds as
follows:
• Player 1 initiates the game by choosing between two actions: Left and Right.
• Depending on Player 1's choice, Player 2 then decides, choosing between two actions,
left (I) and right (`r`).
• Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and
`b`.
The payoffs are determined by the sequence of choices made by all three players. Each
payoff is represented by the triplet (x,y,z), where x, y, and z denote the payoffs for Player 1,
Player 2, and Player 3, respectively. For example, if Player 1 chooses 'Left', Player 2 chooses
'I', and Player 3 chooses `a` the resulting payoff would be (3,1,2). This indicates that Player
1 receives a payoff of $3, Player 2 receives a payoff of $1, and Player 3 receives a payoff of
$2 for this particular sequence of actions.
Left
Player 2
Player 1
Right
Player 2
Player 3
Player 3
Player 3
Player 3
3,1,2
7,4,1 0,3,9
7,3,1 5,6,7
0,0,1 1,6,4
0,4,8
Find the backward-induction equilibrium of this game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1542e5de-e392-4bdb-9d95-e5abdf8e6267%2Faba583c5-d758-484a-8582-31f1bdcc74be%2Fx07zd8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following sequential-move game:
This game involves three players, each making sequential decisions. The game proceeds as
follows:
• Player 1 initiates the game by choosing between two actions: Left and Right.
• Depending on Player 1's choice, Player 2 then decides, choosing between two actions,
left (I) and right (`r`).
• Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and
`b`.
The payoffs are determined by the sequence of choices made by all three players. Each
payoff is represented by the triplet (x,y,z), where x, y, and z denote the payoffs for Player 1,
Player 2, and Player 3, respectively. For example, if Player 1 chooses 'Left', Player 2 chooses
'I', and Player 3 chooses `a` the resulting payoff would be (3,1,2). This indicates that Player
1 receives a payoff of $3, Player 2 receives a payoff of $1, and Player 3 receives a payoff of
$2 for this particular sequence of actions.
Left
Player 2
Player 1
Right
Player 2
Player 3
Player 3
Player 3
Player 3
3,1,2
7,4,1 0,3,9
7,3,1 5,6,7
0,0,1 1,6,4
0,4,8
Find the backward-induction equilibrium of this game.
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