Consider the two player game described by the payoff matric below. L R U 3,3 2,4 D 2,3 1,2 After eliminating strongly dominated strategies, how many outcomes are left? Write your answer as an integer (e.g. 5). [Note that a strategy profile is an outcome, for example (D,R) is an outcome.]
Question
Consider the two player game described by the payoff matric below.
L R U 3,3 2,4 D 2,3 1,2
After eliminating strongly dominated strategies, how many outcomes are left? Write your answer as an integer (e.g. 5). [Note that a strategy profile is an outcome, for example (D,R) is an outcome.]
Solution
To answer this question, we first need to identify if there are any strongly dominated strategies. A strategy is strongly dominated if there is another strategy that always results in a higher payoff, no matter what the other player does.
Looking at the payoff matrix:
L R U 3,3 2,4 D 2,3 1,2
For player 1 (the row player), strategy U is not strongly dominated by D, because the payoff for U is higher against strategy L (3 > 2). Similarly, strategy D is not strongly dominated by U, because the payoff for D is higher against strategy R (2 > 1).
For player 2 (the column player), strategy L is not strongly dominated by R, because the payoff for L is higher against strategy U (3 > 4). Similarly, strategy R is not strongly dominated by L, because the payoff for R is higher against strategy D (3 > 2).
Since there are no strongly dominated strategies, all four outcomes (U,L), (U,R), (D,L), and (D,R) are still possible. Therefore, the answer is 4.
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