QUESTION 4Which of the following is FALSE? A. Every strongly dominant action is weakly dominant B. Every 2-person game has an agent who has a weakly dominant action C. A weakly dominant action need not be strongly dominant
Question
QUESTION 4Which of the following is FALSE? A. Every strongly dominant action is weakly dominant B. Every 2-person game has an agent who has a weakly dominant action C. A weakly dominant action need not be strongly dominant
Solution
To determine which statement is false, let's analyze each option:
A. Every strongly dominant action is weakly dominant. This statement is true. If an action is strongly dominant, it means that it yields a higher payoff than any other action, regardless of what the other player does. Therefore, it is also weakly dominant because it is always at least as good as any other action.
B. Every 2-person game has an agent who has a weakly dominant action. This statement is true. In a 2-person game, each player has a set of actions to choose from. At least one of the players will have a weakly dominant action, meaning that it is always at least as good as any other action they can choose.
C. A weakly dominant action need not be strongly dominant. This statement is false. If an action is weakly dominant, it means that it is always at least as good as any other action. Therefore, it is also strongly dominant because it yields a higher payoff than any other action, regardless of what the other player does.
Based on the analysis, the false statement is C. A weakly dominant action need not be strongly dominant.
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