Discuss the concept of mixed strategy in game theory.

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Discuss the concept of mixed strategy in game theory.

In game theory, a mixed strategy refers to a strategy where a player does not choose a single action with certainty, but instead assigns probabilities to different actions. This means that the player will randomly select actions based on these probabilities. The concept of mixed strategy is used when there is uncertainty about the actions of other players or when there is a need to create unpredictability in order to gain an advantage. By using a mixed strategy, players can introduce randomness into their decision-making process, making it more difficult for opponents to predict their actions and formulate effective counter-strategies. Mixed strategies are often represented by probability distributions over the set of possible actions, and the optimal mixed strategy is determined by finding the probabilities that maximize the player's expected payoff.