Dominant strategies are such strategies which a player would chose regardless of what the other player chooses. In other words, Dominant Strategy provides a higher payoff in any situation as compared to other strategies.
If we revert back to the Prisoner’s Dilemma Problem, we can see that for Prisoner 1, to “Confess” earns a greater payoff than “Remaining Silent” in both Scenarios i.e.
1. If Prisoner 2 Confesses
2. If Prisoner 2 Remain Silent
So in Scenario 1, if Prisoner 1 Confesses, he gets imprisonment for 5 years where as if he Remains Silent, he gets it for 20 years and 5 is better than 20. In Scenario 2, if Prisoner 1 confesses he gets to leave immediately whereas if he Remains Silent, he gets the punishment for 1 year. Again 0 is better than 1. Since 5 is better than 20 and 0 is better than 1 , it proves that “Confess” is a Superior Strategy for Prisoner 1 than to "Remain Silent.
If both Players have a Dominant Strategy which in this case they do, then the Outcome of the game is said to be Dominant Strategy Equilibrium
Strictly Dominant and Weakly Dominant Strategies
| Player 1 | Confess | Not Confess |
| Confess | -1,-1 | -9,0 |
| Not Confess | 0,-9 | -6,-6 |
In the game above, we can see that Player 1's Dominant Strategy is Not Confess since 0 is better than -1 and -6 is better than -9. This is Strictly Dominant Strategy of Player 1. However, if -1 is changed to "0" as in the table below, then in Scenario 1, Player 1 would be indifferent between Confess and Not Confess, but in Scenario 2 he would go for Not Confess.
| Player 1 | Confess | Not Confess |
| Confess | 0,-1 | -9,0 |
| Not Confess | 0,-9 | -6,-6 |
Thus, here although Not Confess is a dominant strategy its is "Weakly Dominating" the other strategy.
