Introduction to Game Theory
In game theory, a mixed strategy is a probability distribution over the set of possible actions that a player can take in a game. It is called a 'mixed' strategy because it involves randomness, or mixing, in the choice of actions.
A mixed strategy is used when a player's optimal strategy involves randomizing their actions in order to make it more difficult for their opponent to predict their behavior. For example, in the game of rock-paper-scissors, a player might use a mixed strategy by choosing rock, paper, or scissors with equal probability. By doing this, their opponent cannot predict what their next move will be, and the player gains an advantage.
Mixed strategies can also be used to find Nash equilibria in games where pure strategies do not exist. In these cases, a mixed strategy Nash equilibrium involves each player randomizing their actions in a way that is consistent with their opponent's strategy. For example, in the game of matching pennies, each player's optimal strategy is to choose heads or tails with equal probability, resulting in a mixed strategy Nash equilibrium.
Overall, mixed strategies are an important tool in game theory for modeling situations where randomness plays a role in decision making.
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