Consider the following game. Player 1 has three actions: A, B, C. Player 2 has three actions: a, b.c. Payoffs are as follows: abcA5,38,51,2B2,66,74,5C4,40,29,3Which of the following aciton profile survives the iterated elimination of strongly dominated actions? A. (A,a) B. (B, c) C. (A, b)
Question
Consider the following game. Player 1 has three actions: A, B, C. Player 2 has three actions: a, b.c. Payoffs are as follows: abcA5,38,51,2B2,66,74,5C4,40,29,3Which of the following aciton profile survives the iterated elimination of strongly dominated actions? A. (A,a) B. (B, c) C. (A, b)
Solution
To determine which action profile survives the iterated elimination of strongly dominated actions, we need to analyze the payoffs for each action combination.
First, let's consider action A. The payoffs for Player 1 when choosing A are 5, 2, and 4 for actions a, b, and c respectively. Comparing these payoffs to the payoffs for action B (3, 6, and 0) and action C (8, 4, and 9), we can see that action A is not strongly dominated by any other action for Player 1.
Next, let's consider action a. The payoffs for Player 2 when Player 1 chooses action a are 3, 6, and 4 for actions A, B, and C respectively. Comparing these payoffs to the payoffs for action b (1, 6, and 0) and action c (5, 7, and 2), we can see that action a is not strongly dominated by any other action for Player 2.
Based on this analysis, we can conclude that the action profile (A, a) survives the iterated elimination of strongly dominated actions. Therefore, the correct answer is A. (A, a).
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