Posts Tagged ‘game theory’

The Prisoner’s Dilemma

August 3, 2017

A simple example from game theory shows how two rational individuals might not chose to cooperate if the result for not doing so might be in their favor.

Two prisoners are asked for more information about their common crime. They can each remain silent and thus collude with each other. Or they can confess their participation and thereby incriminate the other prisoner.

Unfortunately there is already enough evidence against them for a sentence, so if they both remain silent they will still serve some time (say 1 year each). However if they both confess they will both serve more time (say 2 years each). And if one confesses but the other remains silent the confessor will serve no time but the betrayed one will serve an even longer sentence (say 3 years)!

The thing to notice is that each prisoner will serve less time if they defect and betray the other prisoner than if they cooperate with them. You might even think the sentences are calculated to promote betrayal!

Further Reading:

https://en.wikipedia.org/wiki/Prisoner%27s_dilemma

https://plato.stanford.edu/entries/prisoner-dilemma/

William Poundstone / Prisoner’s Dilemma: John Von Neumann, game theory, and the Puzzle of the bomb

Note passage from SEP:

The new story suggests that the Prisoner’s Dilemma also occupies a place at the heart of our economic system. It would seem that any market designed to facilitate mutually beneficial exchanges will need to overcome the dilemma or avoid it.

[*10.23]

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