Introduction to Repeated Games in Game Theory
In game theory, a repeated game is a game in which the same game is played repeatedly by the same players. The concept of repeated games is important because it allows players to develop strategies that take into account the possibility of future interactions. In repeated games, players can learn from their opponents' behavior and adjust their own behavior accordingly. Repeated games can be classified into two categories: finite and infinite repeated games.
A finite repeated game is a game that is played a fixed number of times. In a finite repeated game, players can use backward induction to determine the optimal strategy. Backward induction is a process of working backwards to find the optimal strategy by considering what the other player will do in each possible scenario. An example of a finite repeated game is the iterated prisoner's dilemma game.
In an infinite repeated game, the game is played an infinite number of times. In this case, players cannot use backward induction to determine the optimal strategy because there is no end point. Instead, players must use other strategies, such as the Grim Trigger strategy, which involves punishing the other player if they deviate from the agreed-upon strategy.
Overall, understanding the difference between finite and infinite repeated games is crucial in developing effective strategies in game theory.
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