The prisoner's dilemma

Question

Two suspects are held in separate cells and cannot communicate. Each is offered the same deal.

If both stay silent, each serves 1 year.
If one betrays the other and the other stays silent, the betrayer goes free and the silent one serves 10 years.
If both betray, each serves 5 years.

Each suspect cares only about minimising their own sentence.

What does a rational suspect do, and why?
Why is the outcome worse for both than the one they could have had?
What changes if the two will face the same situation many times?

Accepted Answer

Each suspect betrays, and both serve 5 years, even though both staying silent would have cost them only 1 year each. Betrayal dominates. Consider suspect A. If B stays silent, A gets 1 year by staying silent or 0 by betraying: betray. If B betrays, A gets 10 years by staying silent or 5 by betraying: betray. Whatever B does, betraying is better for A. The same holds for B. A move that is best regardless of the other's choice is called a dominant strategy, and here betrayal is dominant for both. The outcome. Both betray and each serves 5 years. This is the game's only Nash equilibrium: neither…

The prisoner's dilemma

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