Introduction to Repeated Games in Game Theory
Game theory is a branch of mathematics that studies how individuals make decisions in competitive situations where the outcome depends on the choices of all players involved.
Repeated games are a special case of game theory in which the same game is played multiple times by the same players.
In repeated games, players can observe the behavior of their opponents and adjust their strategies accordingly. This creates a more complex decision-making process than in one-shot games, where players must make decisions without knowledge of their opponents' previous choices. Repeated games can also lead to different outcomes than one-shot games, as players may choose to cooperate or defect based on their expected future interactions.
One example of a repeated game is the Prisoner's Dilemma. In this game, two prisoners are arrested and held in separate cells. They are both given the option to either confess or remain silent. If both confess, they both receive a moderate sentence. If one confesses and the other remains silent, the confessor goes free while the other receives a harsh sentence. If both remain silent, they both receive a light sentence. In a one-shot game, the dominant strategy for each player is to confess, as this leads to a moderate sentence regardless of the other player's choice. However, in a repeated game, players may choose to cooperate and remain silent, as this can lead to a better overall outcome.
Overall, repeated games are an important area of study in game theory, as they provide insights into how individuals make decisions over time in competitive situations. Understanding the strategies and outcomes of repeated games can help individuals make better decisions in real-world situations where they will be interacting with the same players multiple times.
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