up some problems. Nowak and Sigmund’s model of indirect reciprocity was criticized by several other experts who pointed out that it was unlikely to work except in very small groups. When I next encountered Nowak, in 2004 at a complexity conference in Boston, his story had grown more elaborate.
In his talk, Nowak recounted the role of the Prisoner’s Dilemma game in analyzing evolutionary cooperation. The essential backdrop was a famous game theory tournament held in 1980, organized by the political scientist Robert Axelrod at the University of Michigan. Axelrod conceived the brilliant idea of testing the skill of game theoreticians themselves in a Prisoner’s Dilemma contest. He invited game theory experts to submit a strategy for playing Prisoner’s Dilemma (in the form of a computer program) and then let the programs battle it out in a round-robin competition. Each program played repeated games against each of the other programs to determine which strategy would be the most “fit” in the Darwinian sense.
Of the 14 strategies submitted, the winner was the simplest— an imitative approach called tit for tat, submitted by the game theorist Anatol Rapoport.15 In a tit-for-tat strategy, a player begins by cooperating in the first round of the game. After that, the player does whatever its opponent did in the preceding round. If the other player cooperates, the tit-for-tat player does also. Whenever the opponent defects, though, the tit-for-tat player defects on the next play and continues to defect until the opponent cooperates again.
In any given series of games against a particular opponent, tit for tat is likely to lose. But in a large number of rounds versus many different opposition strategies, tit for tat outperforms the others on average. Or at least it did in Axelrod’s tournament.
Once tit for tat emerged as the winner, it seemed possible that even better strategies might be developed. So Axelrod held a second tournament, this time attracting 62 entries. Of the contestants in the second tournament, only one entered tit for tat. It was Rapoport, and he won again.
You can see how playing tit for tat enhances opportunities for