Game theory is the study of decision making in interactive situations where the outcome of one person's decision depends on the decisions of others. It is used in economics, political science, psychology, and other fields to study a wide range of topics, including competition, cooperation, negotiation, and voting.

Types of Games

In game theory, a game is any situation where players make decisions that affect each other's payoffs. Each player has a set of possible actions, and the outcome of the game depends on the actions of all players.

There are two main types of games in game theory:

1. Cooperative games: players can communicate and make agreements about how to play the game.
2. Non-cooperative games: players cannot communicate and must make their decisions independently.

Nash Equilibrium

One of the most important concepts in game theory is the Nash equilibrium, named after John Nash, who won the Nobel Prize in Economics in 1994 for his work on game theory. A Nash equilibrium is a set of strategies, one for each player, where no player can improve their payoff by unilaterally changing their strategy.

Mixed Strategies

Mixed strategies are a type of strategy in game theory where a player chooses among two or more pure strategies randomly, according to a probability distribution. A probability distribution is a function that assigns a probability to each possible outcome. Mixed strategies are used when there is no dominant strategy, which is a strategy that is always better than any other strategy, regardless of what the other player does. Mixed strategies can lead to more complex and interesting outcomes in games than pure strategies.

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