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:
“A stated truth loses its grace, but a repeated error appears insipid and ridiculous.”
—Johann Wolfgang Von Goethe (1749–1832)
“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)
“A sympathetic person is placed in the dilemma of a swimmer among drowning men, who all catch at him, and if he give so much as a leg or a finger, they will drown him. They wish to be saved from the mischief of their vices, but not from their vices.”
—Ralph Waldo Emerson (1803–1882)