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Repeated games and cooperation

The prisoner's dilemma looks like a proof that cooperation is irrational. Yet people, firms, and animals cooperate constantly. The missing ingredient is not goodness but the future.

The shadow of the future

Play the dilemma once and defection is unanswerable. Play it repeatedly against the same partner and everything changes, because today's choice affects how they treat you tomorrow. Defecting now wins a small immediate gain and buys a long run of retaliation. If the relationship is likely to continue, that trade is a bad one.

The key quantity is how much the future counts, which depends on the chance of meeting again and on how heavily you discount what is to come. Cooperation becomes sustainable when the shadow of the future is long enough that a lasting stream of mutual cooperation beats a one-off betrayal.

The tournament

In 1980 Robert Axelrod invited game theorists to submit computer strategies to play the repeated dilemma against each other, and ran them in a round robin. Entries arrived with elaborate models of opponent behaviour and probabilistic traps.

The winner, submitted by Anatol Rapoport, was the shortest program entered. Tit for tat cooperates on the first move, then simply copies whatever the opponent did last time. Axelrod announced the result, invited a second round in which everyone knew what had won, and tit for tat won again.

Why such a simple rule wins

Axelrod picked out the properties that did well. The winning strategy was nice: it never defected first, so it never started a feud. It was retaliatory: it punished defection immediately, so it could not be exploited. It was forgiving: one cooperative move from the opponent restored cooperation at once, so mistakes did not spiral. And it was clear: an opponent could work out the rule in two moves, which made cooperating with it visibly worthwhile.

Notice what is absent. Tit for tat never scores more than its opponent in any single encounter. It wins the tournament not by beating its partners but by finding partners to prosper alongside.

What this explains

The result reframes cooperation as something that can emerge among self-interested players, with no altruism, authority, or trust required, provided interactions repeat and defection is answered.

It also explains why cooperation collapses where it does. Anonymity removes the ability to retaliate. One-off dealings remove the future. And a known final round unravels the whole structure from the end backwards, since there is no tomorrow left in which to be punished. Institutions that sustain cooperation, from reputation systems to repeat business to enforceable contracts, are all in the business of restoring one of those missing pieces.