What Is the Prisoner's Dilemma? Why Rational People Fail to Cooperate

Look at the choice from one prisoner's side. If the partner confesses, confessing gets five years instead of ten. If the partner stays silent, confessing gets freedom instead of one year. Whatever the other does, confessing is better, which makes it what game theorists call a dominant strategy. Both prisoners reason the same way, both confess, and both land on the outcome that is worse for each of them than mutual silence.

The point is not that the prisoners are stupid or greedy. Each is doing the best they can given what the other might do, and the trap is in the structure: an outcome that is best for the pair is unreachable by two people who cannot trust each other and cannot enforce a promise. The game was devised in 1950 by two mathematicians at the RAND Corporation, Merrill Flood and Melvin Dresher, and given its story by Albert Tucker, and it was studied first because it looked like the nuclear arms race.

Once you know the pattern you see it constantly. Two countries would each be safer spending less on weapons, but each is safer still if it arms while the other disarms, so both arm. Two petrol stations on the same road would both make more money at a high price, but each can grab the other's customers by cutting, so both cut. Fishing fleets on a shared stock, farmers pumping a shared aquifer, neighbours deciding whether to clear the snow from a shared path, students deciding whether to do their share of a group project: in each case defecting is individually best and collectively ruinous. The ingredients:

• •Two or more players who each choose between cooperating and defecting
• •Defecting beats cooperating whatever the other player does
• •Mutual cooperation beats mutual defection for everyone
• •No way to bind the other player to a promise

Everything changes when the game repeats. If the two players will meet again, indefinitely, a defection today can be punished tomorrow, and cooperation can be rewarded, so the calculation is no longer about one move but about a relationship. In 1980 the political scientist Robert Axelrod invited game theorists to submit computer programs to play repeated prisoner's dilemmas against each other in a tournament. The winner, submitted by Anatol Rapoport, was four lines long. Tit for tat cooperated on the first move and then simply did whatever its opponent had done on the previous one.

It won both tournaments, against far more elaborate rivals, and Axelrod drew out why. It was nice, never defecting first. It was retaliatory, punishing a defection immediately. It was forgiving, returning to cooperation as soon as the other did. And it was clear, so opponents could learn quickly that cooperating with it paid. Later work found that in a noisy world, where moves are sometimes misread, a slightly more forgiving version does better still, because pure tit for tat can lock two well-meaning players into endless mutual revenge over one mistake.

Biologists took up the game to explain how cooperation could evolve among self-interested organisms. Vampire bats share blood meals with roost-mates who fed them in the past and refuse those who did not. Cleaner fish and their clients, and the reciprocal grooming of primates, follow the same logic. The conditions are the ones Axelrod identified: individuals that meet repeatedly, can recognise each other and remember. Where those conditions fail, among strangers who will never meet again, cooperation collapses, which is why anonymity brings out the worst in people and why reputation systems, from village gossip to online reviews, are attempts to make a one-shot game into a repeated one.

Since the trap is structural, the escapes are structural too. Change the payoffs, so that defection is punished by a court, a regulator or a contract, and the dominant strategy disappears; that is what a cartel does illegally and an arms control treaty with inspections does legally. Make the game repeated and visible, so that reputation matters. Reduce the number of players, since cooperation is far easier among two than among two hundred. Or change what the players value: people who care about fairness, or about the other player, are not playing the pure game at all, and in laboratory experiments a large fraction of people cooperate in one-shot dilemmas when the theory says they should not. Human beings, it turns out, are worse at being rational than the model and better at being decent.

Once people learn the prisoner's dilemma, they tend to see it everywhere, but game theorists distinguish several different traps that look alike on the surface. In the stag hunt, a story drawn from Rousseau, two hunters can work together to catch a stag or each go off alone to catch a hare. The stag is better for both, but only if both commit; a hare is safe whatever the other does. Unlike the prisoner's dilemma, cooperating is the best choice if you trust your partner, so the problem is confidence rather than temptation.

The game of chicken has a different shape again. Two drivers speed towards each other, and whoever swerves loses face, but if neither swerves both crash. Here the worst outcome is mutual defiance, so each hopes to convince the other that they will not back down, which is why the game is used to describe tense confrontations between nuclear powers. The distinction matters in practice. Fixing a stag hunt needs reassurance and communication, fixing chicken needs ways for someone to back down without humiliation, and fixing a true prisoner's dilemma needs enforcement or repeated dealings.

One of the most striking real examples comes from the Western Front in the First World War. Small units faced the same enemy across no man's land for weeks at a time, and each side was under orders to kill as many of the other as it could. Yet historians, drawing on soldiers' letters and diaries, have documented a widespread system of unofficial restraint. Artillery fired at the same times and places every day, so the other side knew where not to be; snipers aimed high; meal times and supply routes were left alone. A breach brought measured retaliation, after which the quiet often returned.

Axelrod made the case a centrepiece of his book on cooperation, building on the work of the historian Tony Ashworth, because it had every ingredient the theory predicts. The same small groups met repeatedly, could recognise each other's behaviour, and could punish a defection the next day. High command, which disliked these tacit truces, broke them in ways the theory would also predict. Ordering raids forced lethal contact that the other side felt bound to avenge, and rotating units replaced a long relationship with a series of encounters between strangers, turning a repeated game back into something much closer to a single round.

A British game show called Golden Balls ended each episode with a version of the prisoner's dilemma played for real money. The two finalists each secretly chose to split or steal the jackpot. If both split, they shared it; if one stole while the other split, the stealer took everything; if both stole, both left with nothing.

In one famous episode broadcast in 2008, a player named Nick told his opponent he would definitely steal, but promised to share the money with him afterwards, which left the other player no better choice than to split. When the balls were opened, Nick had chosen split too, and they shared the prize. Game theorists enjoyed the clip because his announcement changed the structure of the game rather than simply bargaining within it.

The prisoner's dilemma is a situation in which each player does better by defecting whatever the other does, yet mutual defection leaves both worse off than mutual cooperation. It describes arms races, price wars and shared resources, and its lesson is that cooperation among the self-interested needs repetition, reputation, enforceable promises or values that go beyond the payoff table.