Prisoner’s dilemma

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Pay-off table

A cooperates

A defects

B cooperates

A gets 1 year
B gets 1 year

A goes free
B gets 3 years

B defects

A gets 3 years
B goes free

A gets 2 years
B gets 2 years

An exercise in calculating economic outcomes by means of metaphor.

Two people are arrested and charged with a conspiracy[1]. Each is held separately in solitary confinement. The two cannot communicate. The authorities have enough evidence to convict both on a lesser charge, but not the main charge. The authorities go to each prisoner separately and offer each the same bargain if she agrees to inform on her co-conspirator. The offer is:

  • If A informs B but B refuses to inform on A:
    • A will not be prosecuted on the lesser charge and will go free
    • B will be prosecuted on the main charge and serve a three year sentence
  • If A informs B and B informs on A:
    • A will serve a two year sentence
    • B will serve a two year sentence
  • If A refuses to inform on B and B refuses to inform on A:
    • A will serve a one year sentence (on the lesser charge).
    • B will serve a one year sentence (on the lesser charge).



References

  1. Whether or not they are guilty is beside the point. If it helps you empathise with their predicament, assume they’re innocent