Introduction to Game Theory
In game theory, a repeated game is a situation in which a particular game is played multiple times between the same players. This is in contrast to a one-shot game, in which the game is played only once. The concept of repeated games is important in game theory because it allows for the exploration of strategies that may not be effective in a one-shot game, but can be successful in a repeated game scenario.
One of the most famous examples of a repeated game is the Prisoner's Dilemma. In this game, two players are given a choice to either cooperate with each other or betray each other. If both players cooperate, they both receive a reward. If both players betray, they both receive a punishment. However, if one player betrays while the other cooperates, the betrayer receives a larger reward while the cooperator receives a larger punishment. In a one-shot game, it is rational for both players to betray, as they cannot rely on the other player to cooperate. However, in a repeated game scenario, strategies such as tit-for-tat can be successful. In tit-for-tat, a player starts by cooperating and then repeats the other player's previous action in subsequent rounds. This allows for cooperation to be established and maintained over multiple rounds.
Another example of a repeated game is the Ultimatum Game. In this game, one player is given a sum of money and must divide it with another player, who can either accept or reject the offer. If the offer is accepted, both players receive the agreed upon amounts. If the offer is rejected, neither player receives any money. In a one-shot game, it is rational for the first player to offer the smallest amount possible, as any amount above zero is a gain. However, in a repeated game scenario, the second player can punish the first player by rejecting any unfair offers. This can lead to more equitable outcomes over multiple rounds.
Overall, repeated games allow for the exploration of strategies that may not be effective in a one-shot game. By playing the same game multiple times, players can establish trust and cooperation, leading to more favorable outcomes for both parties.
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