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Tit for Tat is a highly-effective strategy in game theory for the iterated prisoner's dilemma. It was first introduced by Anatol Rapoport in Robert Axelrod's 1984 tournament. Based on the English saying meaning "equivalent retaliation" ("tip for tap"), an agent using this strategy will respond in kind to a previous opponent's action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not.
This strategy is dependent on four conditions that has allowed it to become the most prevalent strategy for the Prisoner's Dilemma:
- Unless provoked, the agent will always cooperate
- If provoked, the agent will retaliate
- The agent is quick to forgive
- The agent must have a 2/3 chance of competing against the opponent more than once.
For several decades Tit for Tat was the most effective strategy for playing the game, winning in annual automated tournaments against (generally far more complex) strategies created by teams of computer scientists, economists, and psychologists. Game theorists informally believed the strategy to be optimal (although no proof was presented).
In a 2004 tournament Tit for Tat was beaten for the first time. A strategy created by the University of Southampton detected (by means of a pre-arranged pattern of seemingly random operations) whether its counterpart was another instance of the Southampton strategy. In cases where the counterpart is determined not to be using the Southampton strategy, it acts as a spoiler for the non-Southampton player. In cases where it is, the two form a master-slave relationship, where the slave sacrifices itself for the master by always cooperating and letting the master get away with never cooperating, which maximises the number of points for the master. In the competition where hundreds of agents are entered and compete against each other, Southampton entered 60 agents, guaranteeing that a few master agents gain incredibly high scores by sacrificing the rest of the slaves agents to the bottom of the score list.
More general implications
The success of the strategy, which is largely cooperative, took many by surprise. In successive competitions various teams produced complex strategies which attempted to "cheat" in a variety of cunning ways, but Tit for Tat eventually prevailed in every competition.
Some theorists believe this result may give insight into how groups of animals (and particularly human societies) have come to live in largely (or entirely) cooperative societies, rather than the individualistic "red in tooth and claw" way that might be expected from individual engaged in a Darwinian struggle. This, and particularly its application to human society and politics, is the subject of Robert Axelrod's book The Evolution of Cooperation.
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