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.) Dob Not Dob Dob -6,-6 0,-8 Not Dob -8,0 X,XSuggest one value in the range that makes this game a Prisoner's Dilemma.Enter your answer as a single number between -100 and 100.
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.) Dob Not Dob Dob -6,-6 0,-8 Not Dob -8,0 X,XSuggest one value in the range that makes this game a Prisoner's Dilemma.Enter your answer as a single number between -100 and 100.
Solution
The game matrix you provided is as follows:
| Dob | Not Dob | |
|---|---|---|
| Dob | -6,-6 | 0,-8 |
| Not Dob | -8,0 | X,X |
In a Prisoner's Dilemma game, each player has a dominant strategy that leads to a less than optimal outcome for both. In this case, the dominant strategy for both players is to "Not Dob".
The payoff for both players when they both choose "Not Dob" is X. For this game to be a Prisoner's Dilemma, X must be greater than -8 (the payoff when Player 1 chooses "Not Dob" and Player 2 chooses "Dob") and less than 0 (the payoff when Player 1 chooses "Dob" and Player 2 chooses "Not Dob").
So, any value of X in the range (-8, 0) would make this game a Prisoner's Dilemma. For example, X could be -1.
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