# What Is a Dominant Strategy in Game Theory?

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Diego Sanchez

Game theory is a mathematical framework used to analyze and understand strategic interactions between individuals or groups. One of the key concepts in game theory is the idea of a dominant strategy.

A dominant strategy is a choice that will always yield the best outcome for a player, regardless of what other players do. In other words, it is the best option regardless of how others behave.

## Example

Let’s consider an example of two friends, Alice and Bob, playing a game. They have to choose between two options: A or B.

If Alice chooses A and Bob chooses A, they both receive 5 points. If Alice chooses A and Bob chooses B, Alice gets 1 point and Bob gets 10 points.

If Alice chooses B and Bob chooses A, Alice gets 10 points and Bob gets 1 point. If Alice chooses B and Bob chooses B, they both receive 0 points.

### Dominant Strategy

In this scenario, we can see that if Bob were to choose option A regardless of what Alice chose, it would be his dominant strategy.

If Bob plays A no matter what Alice does:
– If Alice plays A: he will get 5 points
– If Alice plays B: he will get 1 point

Conversely, if Alice were to choose option A regardless of what Bob chose, it would be her dominant strategy as well.

Thus in this particular example scenario both players have a dominant strategy which is “A”.

### Nash Equilibrium

When every player in a game uses their dominant strategy then it results in Nash equilibrium. This means that no player can improve their own outcome by changing their decision while others remain unchanged.

## Conclusion

Dominant strategies are important in game theory because they simplify decision-making for players. It helps to determine the most optimal strategies for each player in a game. Understanding and identifying dominant strategies can help individuals make better decisions in various fields such as economics, politics, and social sciences.