prisoner's dilemma
/ PRIZ-nerz dih-LEM-uh /
Two partners in crime are arrested and locked in separate rooms, unable to talk. The police offer each the same deal: betray your partner and you'll go easy, stay silent and you risk a long sentence if the other talks. If both stay silent, the police can only prove a minor charge, so each gets a light sentence. If both betray, each gets a medium sentence. But if one betrays while the other stays silent, the betrayer walks free and the silent one takes the heavy fall. What should each prisoner do? This little story, set up by Merrill Flood and Melvin Dresher and dramatized by Albert Tucker around 1950, is the most famous puzzle in all of game theory.
Work through one prisoner's logic. 'If my partner stays silent, I go free by betraying instead of getting a light sentence — so I should betray. If my partner betrays, I get a medium sentence by betraying versus the heavy fall by staying silent — so again I should betray.' Betraying is a dominant strategy: it is better no matter what the other does. The same reasoning grips the partner. So both betray and both get the medium sentence — even though if they had both stayed silent, both would have been better off. The maddening result is a Nash equilibrium (neither can improve alone) that is worse for everyone than cooperation.
The prisoner's dilemma is a model of a vast class of real conflicts where individual self-interest sabotages the common good. Two firms in a price war both cut prices and erode profits; two countries both build weapons and end up no safer but poorer; everyone overfishes the same sea until it empties. Recognizing a situation as a prisoner's dilemma reframes the question from 'who is being foolish?' to 'how can we change the rules — through contracts, regulation, or repeated dealings — so that cooperating becomes the rational choice?'
Two competing supermarkets each weigh whether to launch a price-cut blitz. If neither does, both keep healthy margins. If one does, it steals customers — so the other matches. They both cut, shoppers win, but both stores' profits sink to where they were before, only thinner. They are trapped in a prisoner's dilemma despite each acting 'rationally'.
A supermarket price war: each store's rational cut leaves both worse off — a prisoner's dilemma.
The trap holds only if the game is played once with no way to enforce a deal. When the same players interact repeatedly, cooperation can emerge — which is why repeated games and reputation matter so much.