Game theory is a fascinating branch of mathematics that deals with decision making in situations where there are multiple players involved. Pure strategy refers to a course of action that a player will take with certainty when playing a game. In this article, we will explore in detail what pure strategies are in game theory and why they are important.

## What are Pure Strategies?

In game theory, a pure strategy is a complete plan of action for a player that specifies every move they will make during the game. It is called “pure” because the player is certain about what they will do, regardless of any other factors. That means if all players play their pure strategies, the outcome of the game can be predicted with certainty.

### Example:

Let’s consider an example to understand this better. Suppose two players, A and B, are playing a game where each has two options: to cooperate or not cooperate. If both players cooperate, they get a reward of 5 points each; if both do not cooperate, they get no points; and if one cooperates while the other does not, the non-cooperating player gets 10 points while the cooperating player gets nothing.

Now suppose Player A decides to always cooperate no matter what Player B does. This is Player A’s pure strategy.

Similarly, let’s say Player B also decides to always cooperate no matter what Player A does. This is Player B’s pure strategy as well.

If both players stick to their pure strategies and always cooperate, they will both receive 5 points each – this is called the Nash equilibrium in this situation.

## Why are Pure Strategies Important?

Pure strategies are important because they allow us to analyze games more easily and predict outcomes with certainty. They help us understand how rational players would behave in different situations and what choices would lead to an optimal outcome for everyone involved.

Moreover, by using pure strategies, we can identify the Nash equilibrium of a game, which is the most stable outcome where no player has any incentive to change their strategy. This is crucial in understanding the behavior of players in a game and how they interact with each other.

## Conclusion

Pure strategies are an essential concept in game theory that allow us to analyze games more easily and predict outcomes with certainty.

By using pure strategies, we can identify the Nash equilibrium of a game, which is the most stable outcome where no player has any incentive to change their strategy.

In conclusion, pure strategies provide us with a solid foundation for analyzing games and understanding how players make decisions. If you’re interested in learning more about game theory, studying pure strategies is an excellent place to start!