# What Is a Mixed Strategy Game Theory?

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Diego Sanchez

In game theory, a mixed strategy refers to a player’s behavior when they choose to randomize their actions instead of sticking to a single strategy. In other words, instead of always playing the same move in response to a certain situation, players will sometimes choose a different action at random. Mixed strategies can be difficult to analyze, but they are an important part of game theory and can help predict outcomes in complex situations.

## What is Game Theory?

Game theory is the study of how people make decisions. It is used in economics, political science, psychology, and other fields to understand how people interact with each other in social situations. In game theory, players are assumed to be rational and self-interested, meaning that they will always act in a way that benefits themselves the most.

## What is a Strategy?

In game theory, a strategy is a plan of action that a player chooses in order to achieve their goals. A strategy can be simple or complex and can involve multiple steps or decisions. A player’s strategy depends on their goals and the actions of other players.

## What is a Pure Strategy?

A pure strategy is when a player always chooses the same action in response to a certain situation. For example, if you always choose “rock” in rock-paper-scissors, then “rock” is your pure strategy. Pure strategies are easy to analyze because there are no random elements involved.

## What is a Mixed Strategy?

A mixed strategy is when a player chooses different actions at random instead of sticking with one pure strategy. For example, if you sometimes choose “rock,” sometimes choose “paper,” and sometimes choose “scissors” in rock-paper-scissors at random, then you are using a mixed strategy. The use of mixed strategies makes it more difficult for opponents to predict your moves.

## How are Mixed Strategies Analyzed?

Mixed strategies can be analyzed using probability theory. When a player uses a mixed strategy, the probability of each action being chosen is determined by the player’s preferences and the actions of other players. By calculating the probabilities of each possible outcome, game theorists can predict the likely result of a given situation.