Tit for tat

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Tit for tat is an English saying meaning "equivalent retaliation". It is also a highly effective strategy in game theory for the iterated prisoner's dilemma. It was first introduced by Anatol Rapoport in Robert Axelrod's two tournaments, held around 1980. An agent using this strategy will initially cooperate, then respond in kind to an opponent's previous action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is similar to superrationality and reciprocal altruism in biology.

Overview

This strategy is dependent on four conditions, which have allowed it to become the most successful strategy for the iterated prisoner's dilemma:

1. Unless provoked, the agent will always cooperate
2. If provoked, the agent will retaliate
3. The agent is quick to forgive
4. The agent must have a good chance of competing against the opponent more than once.

In the last condition, the definition of "good chance" depends on the payoff matrix of the prisoner's dilemma. The important thing is that the competition continues long enough for repeated punishment and forgiveness to generate a long-term payoff higher than the possible loss from cooperating initially.

Implications

In a population where tit for tat is a common strategy, two lessons can be learned:

1. The society will be overall better off, if it actively supports cooperation and motivates not to defect.
2. For the society, it is very important to know the perceptions of its members about tit for tat situation: whether people think that others will cooperate, or whether people think that others will defect. If a critical mass of people move from cooperation to defect, the society may rapidly and surprisingly (unless this phenomenon is understood and monitored) enter and be trapped in a vicious cycle of defections.

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