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Game Theory: The Prisoner's Dilemma

Playing More Than Once

In the basic version the prisoners only play once, so there's no reason to trust each other. But a lot of real situations repeat, like two companies competing every year. When the same two players meet again and again, the game changes, because what you do today affects how the other player treats you tomorrow.

Axelrod's Tournament

In 1980 the political scientist Robert Axelrod invited people to send in computer programs that would play a repeated prisoner's dilemma against each other. Every program played every other program over many rounds, and the points were added up at the end. Some of the entries were long and complicated, but the winner was one of the shortest, a strategy called tit for tat, sent in by Anatol Rapoport.

Tit for tat is really simple. It cooperates in the first round, and after that it just copies whatever the other player did in the round before. Axelrod ran a second, bigger tournament after publishing the results, and tit for tat won again.

Table of 6 rounds where tit for tat copies the other player's move from the round before

Tit for tat against a player who defects once in round 3.

Why It Works

Axelrod pointed out a few things that made tit for tat do so well. It is nice, meaning it never defects first. It retaliates, so it can't be taken advantage of for long. It forgives, going back to cooperating as soon as the other player does. And it is clear, so other programs could easily figure out what it was doing and learn that cooperating pays.

The bigger lesson is that cooperation can come about without anyone forcing it, as long as the players expect to meet again. Axelrod called this the shadow of the future.