Consider the two player game described by the payoff matric below. L R U 3,3 2,x D 2,3 1,2 What value must x NOT BE for the iterative elimination of strongly dominated strategies to lead to a single outcome? Write your answer as an integer (e.g. 5).
Question
Consider the two player game described by the payoff matric below.
L R U 3,3 2,x D 2,3 1,2
What value must x NOT BE for the iterative elimination of strongly dominated strategies to lead to a single outcome? Write your answer as an integer (e.g. 5).
Solution
The iterative elimination of strongly dominated strategies in a game involves removing strategies that are always worse than another strategy, regardless of what the other player does.
In the given payoff matrix, we can see that for Player 2, the strategy 'R' is dominated by 'L' if the payoff of 'L' is always greater than 'R'. This happens when x < 3.
For Player 1, the strategy 'D' is dominated by 'U' if the payoff of 'U' is always greater than 'D'. This is always the case in the given matrix.
So, if x < 3, we can eliminate the dominated strategies 'R' for Player 2 and 'D' for Player 1, leading to a single outcome (U,L).
However, if x = 3, then 'R' is no longer dominated by 'L' for Player 2, and we cannot eliminate any strategies, leading to multiple possible outcomes.
Therefore, the value that x must NOT BE for the iterative elimination of strongly dominated strategies to lead to a single outcome is 3.
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