If you've ever played a game, whether it's chess, poker, or even rock-paper-scissors, you've used some form of strategy. In game theory, a pure strategy is a set of choices that a player can make in a game that will lead to a specific outcome.
What is Game Theory?
Game theory is a branch of mathematics that studies decision-making in situations where two or more individuals or groups have competing interests. Game theory has many applications, from economics and business to psychology and political science.
In game theory, a game is any situation where two or more players have to make choices that affect each other's outcomes. The players can be individuals, groups, or even nations.
What is a Pure Strategy?
A pure strategy in game theory is a set of choices that a player can make in a game that will lead to a specific outcome. In other words, a pure strategy is a specific set of actions that a player will take in a game, regardless of what their opponent does.
For example, in rock-paper-scissors, a player's pure strategy could be to always choose rock. This means that no matter what their opponent chooses, the player will always choose rock. This is a pure strategy because the player is not changing their choice based on what their opponent does.
Types of Pure Strategies
There are three types of pure strategies in game theory: dominant strategy, dominated strategy, and Nash equilibrium.
Dominant Strategy
A dominant strategy is a pure strategy that is always the best choice for a player, regardless of what their opponent does. In other words, no matter what their opponent does, the player's dominant strategy will always lead to the best outcome for them.
For example, in a game of Prisoner's Dilemma, a player's dominant strategy would be to betray their partner, regardless of whether their partner betrays them or not.
Dominated Strategy
A dominated strategy is a pure strategy that is always the worst choice for a player, regardless of what their opponent does. In other words, no matter what their opponent does, the player's dominated strategy will always lead to the worst outcome for them.
For example, in a game of Prisoner's Dilemma, a player's dominated strategy would be to cooperate with their partner, regardless of whether their partner betrays them or not.
Nash Equilibrium
A Nash equilibrium is a pure strategy that is the best response for both players in a game. In other words, each player's Nash equilibrium strategy is the one that will lead to the best outcome for them, given what their opponent does.
For example, in a game of Rock-Paper-Scissors, each player's Nash equilibrium strategy is to choose each option with equal probability. This means that each player has an equal chance of winning, and no player can improve their outcome by changing their strategy.
Conclusion
Pure strategies are an important concept in game theory, as they help us understand how players make decisions in games. Whether you're playing a simple game with friends or analyzing complex economic systems, understanding pure strategies can help you make better decisions and improve your outcomes.
