In game theory, a strictly dominant strategy is a decision-making approach that allows players to choose the best possible option regardless of the choices made by other players. It is an essential concept in game theory that helps players make rational decisions in various situations.

Understanding Dominant Strategy

Dominant strategy is a decision-making approach where a player chooses the best possible strategy regardless of other player’s strategies. A strategy is said to be dominant if it provides the maximum benefit to a player, no matter what the other player does.

For example, let’s consider a situation where there are two players, A and B. Each player has two strategies, “Strategy 1” and “Strategy 2.” The payoff matrix for this situation looks like this:

Strategy 1 Strategy 2
Strategy 1 (3,3) (0,4)
Strategy 2 (4,0) (2,2)

In this matrix, the number inside each cell represents the payoff for each player. For instance, if both players choose Strategy 1, then Player A gets three points while Player B gets three points as well.

The Concept of Strictly Dominant Strategy

In some cases, one strategy may be better than all others for one of the players. This type of strategy is called a strictly dominant strategy.

A strictly dominant strategy guarantees that selecting it will always yield better results than choosing any other available strategy, regardless of what the other player chooses.

Let’s consider the same matrix as before, but with one small change. Player B’s payoff for (Strategy 1, Strategy 2) has been increased from four to five.

Strategy 1 Strategy 2
Strategy 1 (3,3) (0,5)
Strategy 2 (4,0) (2,2)

Now, let’s examine Player A’s options. If Player B chooses Strategy 1, then Player A’s best option is to choose Strategy 1 because it yields a payoff of three points.

If Player B selects Strategy 2 instead, then Player A’s best option is still Strategy 1 since it yields a payoff of four points. Therefore, in this case, Strategy 1 is strictly dominant for Player A.

Similarly, let’s examine Player B’s options. If Player A chooses Strategy 1, then Player B’s best option is to choose Strategy 2 because it yields a payoff of five points.

If Player A selects Strategy 2 instead, then Player B’s best option is still to choose Strategy 2 since it yields a payoff of two points. Therefore in this case as well, Strategy 2 is strictly dominant for Player B.

The Importance of Strictly Dominant Strategies in Game Theory

The concept of strictly dominant strategies helps players make rational decisions when there are multiple strategies available. It eliminates the need for players to consider all possible strategies and their potential outcomes, which can be a time-consuming and overwhelming task.

In addition, strictly dominant strategies make it easier for players to anticipate the choices of their opponents. If a player knows that their opponent has a strictly dominant strategy, then they can anticipate their opponent’s decision and adjust their own strategy accordingly.

Conclusion

In game theory, strictly dominant strategy is an approach that allows players to choose the best possible option regardless of other player’s choices. Strictly dominant strategies eliminate the need for extensive analysis of multiple strategies and help players anticipate their opponent’s moves more effectively.