Repeated Prisoner's Dilemma
Although the Prisoner's dilemma has only one Nash equilibrium (everyone defect), cooperation can be sustained in the repeated Prisoner's dilemma if the discount factor is not too low; that is, if the players are interested enough in future outcomes of the game. Strategies known as trigger strategies comprise Nash equilibria of the repeated Prisoner's dilemma. However, Prisoner's dilemma is one where the minmax value is equal to the Nash Equilbrium payoff. This means that a player who knows the exact horizon may just decide to switch to Defect without fear of punishment.
An example of repeated prisoner's dilemma is the WWI trench warfare. Here, though initially it was best to cause as much damage to the other party as possible, as time passed and the opposing parties got to 'know' each other, they realised that causing as much damage as possible to the other by, e.g. artillery will only prompt a similar response: e.g. blowing up the foodstock of the other (through bombardment) will only leave both battalions hungry. After some time, the opposing battalions learned that it is sufficient to show what they are capable of, instead of actually carrying out the act.
Read more about this topic: Repeated Game
Famous quotes containing the words repeated, prisoner and/or dilemma:
“The poem of the mind in the act of finding
What will suffice. It has not always had
To find: the scene was set; it repeated what
Was in the script.
Then the theatre was changed
To something else. Its past was a souvenir.”
—Wallace Stevens (1879–1955)
“That there is also freedom in captivity, only a prisoner can claim. Coming from a prison guard, this statement would be blasphemy.”
—Friedrich Dürrenmatt (1921–1990)
“Many women are surprised by the intensity of their maternal pull and the conflict it brings to their competing roles. This is the precise point at which many women feel the stress of the work/family dilemma most keenly. They realize that they may have a price to pay for wanting to be both professionals and mothers. They feel guilty for not being at work, and angry for being manipulated into feeling this guilt. . . . They don’t quite fit at home. They don’t quite fit at work.”
—Deborah J. Swiss (20th century)