REPEATED GAMES
A game that is played only once is called a “one-shot” game. Repeated games are games that are played over and over again.
Repeated Game = A game in which actions are taken and payoffs received over and over again.
Many oligopolists and real-life relationships can be characterized as a repeated game. Strategies in a repeated game are often more complex than strategies in a one-shot game, as the players need to be concerned about the reactions and potential retaliations of other players. As such, the players in repeated games are likely to choose cooperative or “win-win” strategies more often than in one shot games. Examples include concealed carry gun permits: are you more likely to start a fight in a no-gun establishment, or one that allows concealed carry guns? Franchises such as McDonalds were established to allow consumers to get a common product and consistent quality at locations new to them. This allows consumers to choose a product that they know will be the same, given the repeated game nature of the decision to purchase meals at McDonalds.
FINITELY VS INFINITELY REPEATED GAMES
Repeated games may be broadly divided into two classes, finite and infinite, depending on how long the game is being played for.
Finite games are those in which both players know that the game is being played a specific (and finite) number of rounds, and that the game ends for certain after that many rounds have been played. In general, finite games can be solved by backwards induction.
Infinite games are those in which the game is being played an infinite number of times. A game with an infinite number of rounds is also equivalent (in terms of strategies to play) to a game in which the players in the game do not know for how many rounds the game is being played. Infinite games (or games that are being repeated an unknown number of times) cannot be solved by backwards induction as there is no "last round" to start the backwards induction from.
Even if the game being played in each round is identical, repeating that game a finite or an infinite number of times can, in general, lead to very different outcomes (equilibria), as well as very different optimal strategies.