Consider the two player game described by the payoff matric below. L RU 3,3 2,xD 2,3 1,2What 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
Question
Consider the two player game described by the payoff matric below. L RU 3,3 2,xD 2,3 1,2What 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
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, the strategies for the column player are L and R. The row player's payoffs for these strategies are 3 and 2 for U, and 2 and 1 for D.
For the column player, the payoffs for U and D are 3 and x for L, and 3 and 2 for R.
If x > 3, then L is a strongly dominated strategy for the column player because the payoff for R (3, 2) is always better than the payoff for L (3, x).
If x < 2, then R is a strongly dominated strategy for the column player because the payoff for L (3, x) is always better than the payoff for R (3, 2).
However, if x = 2, then neither L nor R is a strongly dominated strategy because the payoffs for L and R are the same (3, 2).
Therefore, for the iterative elimination of strongly dominated strategies to lead to a single outcome, x must not be equal to 2. So, the answer is 2.
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