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Game Theory

The prisoner's dilemma

Two suspects are arrested and held in separate rooms with no way to communicate. The prosecutor offers each the same deal, and what follows is the most studied situation in social science.

The offer

If you testify against your partner and they stay silent, you walk free and they get ten years. If you both stay silent, the prosecutor can only make a minor charge stick and you each get one year. If you both testify, you each get eight.

Each prisoner has two strategies: cooperate with the other by staying silent, or defect by testifying.

A two-by-two payoff grid for the prisoner's dilemma, with cooperate and defect for each player, showing one year each for mutual cooperation, eight years each for mutual defection, and the zero and ten year split when only one defects.
A two-by-two payoff grid for the prisoner's dilemma, with cooperate and defect for each player, showing one year each for mutual cooperation, eight years each for mutual defection, and the zero and ten year split when only one defects.

The uncomfortable logic

Put yourself in one cell and reason it through. Suppose your partner stays silent. Then testifying gets you zero years instead of one, so you should testify. Now suppose your partner testifies. Then testifying gets you eight years instead of ten, so again you should testify.

Whatever the other does, testifying is better. In the language of the subject, defecting dominates cooperating, and a dominant strategy is one you should play without needing to guess anything about your opponent.

So both defect, and both get eight years. Yet if both had stayed silent they would have got one. Two players, each reasoning impeccably, land on an outcome that is worse for both than one they could plainly see. The result is not a mistake in the reasoning; it is a property of the situation.

Everywhere you look

The structure recurs constantly. Two firms would both profit from keeping prices high, but each gains by undercutting, so both cut. Two nations would both prefer to spend on hospitals rather than missiles, but neither dares disarm alone. A fishing fleet would prosper by leaving enough fish to breed, but any one boat gains by taking more, and the stock collapses.

Each is the same shape: individually rational choices producing a collectively terrible result. Notice that communication alone does not fix it. The prisoners could agree to stay silent through the wall and the logic would be unchanged, because once separated each still does better by breaking the promise. What is missing is not agreement but a reason to keep it.

That is the real lesson, and it points at the escape route. If defecting is individually best, then cooperation needs something that changes the payoffs: a contract, a regulator, a reputation, or a relationship that will outlast today.