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What are Mixed Strategies and Expected Payoff?

Mixed strategies and expected payoffs are key components within game theory, a discipline at the intersection of mathematics and economics course dedicated to understanding decision-making in strategic scenarios.

Game Theory is particularly pertinent in addressing economic problems where individual choices are intricately linked to the actions of others, presenting challenges in predicting outcomes and optimizing strategies.

• In game theory, players often have multiple strategies they can choose from.
• A pure strategy involves selecting one specific action with certainty.
• However, a mixed strategy involves a player randomizing between different pure strategies according to a probability distribution.
• Players choose these probabilities to maximize their expected payoff, considering the possible responses of their opponents.
• Mixed strategies are used when players have no dominant strategy or when it's beneficial to introduce uncertainty to exploit opponent's behavior.

• The expected payoff represents the average payoff a player can expect to receive over time when employing a particular strategy.
• It is calculated by multiplying the payoff associated with each outcome by the probability of that outcome occurring and summing up these values.
• Expected payoff helps players evaluate the effectiveness of their strategies and make informed decisions.
• Players aim to maximize their expected payoff by choosing the strategy that yields the highest average payoff.

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