# What Is Pure Strategy in Game Theory?

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Vincent White

Game theory is a fascinating field that deals with decision-making in interactive situations. It has various applications in economics, political science, psychology, and even biology.

In game theory, pure strategy refers to a specific course of action that a player takes in a game. In this article, we will explore the concept of pure strategy in game theory and its significance.

## What Is Pure Strategy?

In game theory, a pure strategy refers to a specific set of moves or actions that a player chooses to make in a game. It is an unequivocal choice of what move to make at every turn, regardless of the other players’ choices. A pure strategy is thus deterministic and completely defined by the player’s preferences and objectives.

### Examples of Pure Strategies

Let us consider some examples to understand pure strategies better. Suppose two players, A and B, are playing Rock-Paper-Scissors.

If both players always choose rock every time they play, then their strategies are pure strategies. Similarly, if both players always choose scissors or paper every time they play, their strategies would also be pure strategies.

Another example could be two companies competing for market share by choosing prices for their products. If both companies always set the same price for their products no matter what the other company does, then they are following pure strategies.

### Pure Strategy vs Mixed Strategy

A mixed strategy is different from a pure strategy as it involves an element of randomness or probability in decision-making. In a mixed strategy, the player chooses each move with some probability distribution rather than choosing one specific move every time.

For instance, if in Rock-Paper-Scissors game Player A randomly chooses rock 50% of the time and paper 50% of the time while Player B randomly chooses scissors 33% of the time, rock 33% of the time and paper 33% of the time, then they are following mixed strategies.

### Significance of Pure Strategy

Pure strategies are essential in game theory as they help simplify complex decision-making problems. By assuming that players follow pure strategies, we can analyze a game with a finite number of possible outcomes. It allows us to determine the best course of action for each player and predict the outcome of a game.

Moreover, pure strategies are useful in determining Nash equilibrium, which is a concept in game theory that represents a state where no player has an incentive to change their strategy unilaterally. Nash equilibrium is reached when each player’s strategy is optimal given the other players’ strategies.

### Conclusion

In conclusion, pure strategy is an important concept in game theory that refers to a specific set of moves or actions that a player chooses to make in a game. It helps simplify complex decision-making problems and allows us to predict the outcome of a game. Understanding pure strategy is crucial for anyone interested in game theory and decision-making analysis.