In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). The stage game is usually one of the well studied 2 person games. The repeated game can have different equilibrium properties because the threat of retaliation is real, since one will play the game again with the same person. Single stage game or single shot game are names for non-repeated games. Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ... An extensive form game is a specification of a game in game theory. ... Game theory studies strategic interaction between individuals in situations called games. ... In game theory, the Nash equilibrium (named after John Nash who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only their own strategy. ...
Infinitely repeated games
Repeated games may be repeated finitely or infinitely many times. The most widely studied repeated games are games that are repeated a possibly infinite number of times. These games are modeled by applying a discount factor to each future stage. This discount factor has two primary interpretations. First, it might be that at each stage there is some finite probability that the game ends. Second, it might be that each individual cares slightly less about each successive future stage. In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} where is a natural number. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... In finance, discounting is the process of finding the current value of an amount of cash at some future date, and along with compounding cash form the basis of time value of money calculations. ...
Repeated Prisoner's dilemma
Although the Prisoner's dilemma has only one Nash equilibria (everyone defect), cooperation can be sustained in the repeated Prisoner's dilemma. Strategies known as trigger strategies comprise Nash equilibria of the repeated Prisoner's dilemma. This result is part of a larger class of results known as the folk theorem. Many authors believe that this constitutes the explanation for social cooperation. Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game (game in the sense of Game Theory). ... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ...
References
Fudenberg, Drew and Jean Tirole (1993) Game Theory MIT Press.
In game theory, a repeatedgame (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game).
The repeatedgame can have different equilibrium properties because the threat of retaliation is real, since one will play the game again with the same person.
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