In the game below, who has a dominant strategy? As usual, Player 1 is the row player and Player 2 is the column player.
Understand the Problem
The question is asking who has a dominant strategy in the given payoff matrix between two players. A dominant strategy means that a player's choice is the best response regardless of what the other player chooses. The high-level approach will involve analyzing the payoff matrix to determine if either player has a consistently higher payoff regardless of the other's actions.
Answer
Both players.
Answer for screen readers
Both players.
Steps to Solve
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Analyze Payoffs for Player 1
For Player 1 (row player), we will look at their payoffs based on Player 2's choices.- If Player 2 chooses Left:
- Player 1 gets 5 (Top) or 3 (Bottom). → Best choice is Top (5).
- If Player 2 chooses Right:
- Player 1 gets 12 (Top) or 10 (Bottom). → Best choice is Top (12).
- If Player 2 chooses Left:
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Analyze Payoffs for Player 2
Now, we analyze Player 2's payoffs based on Player 1's choices.- If Player 1 chooses Top:
- Player 2 gets 6 (Left) or 5 (Right). → Best choice is Left (6).
- If Player 1 chooses Bottom:
- Player 2 gets 8 (Left) or 7 (Right). → Best choice is Left (8).
- If Player 1 chooses Top:
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Determine Dominant Strategies
- For Player 1:
Player 1's best response is always Top, regardless of Player 2's action. Thus, Player 1 has a dominant strategy. - For Player 2:
Player 2's best response is always Left, regardless of Player 1's action. Thus, Player 2 also has a dominant strategy.
- For Player 1:
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Conclusion
Since both players have a dominant strategy, the answer is "Both players."
Both players.
More Information
In game theory, a dominant strategy exists when one player's strategy yields a higher payoff regardless of the strategies chosen by their opponent. Here, both players consistently prefer their respective strategies (Top and Left) across all possible scenarios in the payoff matrix.
Tips
- Failing to compare each strategy thoroughly for both players.
- Assuming one player has a dominant strategy without checking the other player’s outcomes.
- Misinterpreting the payoff matrix structure, leading to incorrect dominant strategy conclusions.
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