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TIT FOR TAT

July 18, 2009 Leave a comment

In case you missed it, the game theoretical problem known as the prisoner’s dilemma goes something like this:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

Regardless of the other player’s choice, a player will always get the best payoff by defecting. However, if both players follow that logic, they both end up with the worst payoff, a Pareto suboptimal solution.

In the 70s and 80s, pursuing answers to the question ‘given all that, how and why do altruistic (cooperative) strategies develop and survive in nature (ie outside theory)?’, political scientist Robert Axelrod held several iterated prisoner’s dilemma tournaments, in which contributors wrote computer programs to play multiple rounds of PD.

The winning program was called TIT FOR TAT, which was also the simplest program submitted. Basically, TFT cooperates on the first round, and then does whatever the other player did the previous round.

Axelrod’s analysis in his book The Evolution of Cooperation presented 4 characteristics of the winning strategy TFT:
1. nice: don’t be the first to defect
2. provocable: retaliate (to avoid exploitation)
3. not envious: don’t be greedy
4. clear (not clever): don’t try to be too tricky

(It’s probably worth elaborating point #3: TFT can’t actually ever do better than the other player – the best it can ever do is tie. TFT actually won the tournaments not by winning any individual rounds but by coming in a strong second against all the other players. More on Axelrod’s analysis can be found here.)