In this and all other questions in which a game matrix is given, Player 1 chooses the row, Player 2 chooses the column, and if there is a Player 3, she chooses the matrix.) Choose all of below values of X that make strategy D a strongly dominant strategy for Player 1 in the following game. L R T 2,3 -2,-3 D 3,2 X,-2 -3 -2 0 2 3 4
Question
In this and all other questions in which a game matrix is given, Player 1 chooses the row, Player 2 chooses the column, and if there is a Player 3, she chooses the matrix.)
Choose all of below values of X that make strategy D a strongly dominant strategy for Player 1 in the following game.
L R T 2,3 -2,-3 D 3,2 X,-2
-3
-2
0
2
3
4
Solution
A strategy is said to be strongly dominant if, regardless of what any other players do, the strategy earns a player a higher payoff than any other. If the player can do better, no matter what the opponents do, then that strategy is said to be strongly dominant.
In this case, Player 1 has two strategies: T and D. We want to find the values of X that make D a strongly dominant strategy for Player 1. This means that the payoff from D should be higher than the payoff from T, no matter what Player 2 does.
Let's look at the payoffs for Player 1:
- If Player 2 chooses L, Player 1 gets 2 from T and 3 from D. So, D is better than T.
- If Player 2 chooses R, Player 1 gets -2 from T and X from D. For D to be better than T, X should be greater than -2.
So, the values of X that make D a strongly dominant strategy for Player 1 are all values greater than -2. From the given options, these are 0, 2, 3, and 4.
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