Tit for tat

Tit for Tat is a strategy in game theory for the iterated prisoner's dilemma. 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:

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 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, by a modified Tit for Tat strategy which detected (by means of a pre-arranged pattern of seemingly random operations) whereby its counterpart was another instance of the modified strategy. In cases where the counterpart is determined not to be the modified strategy, it defaults to Tit-for-Tat; in cases where it is, the two always cooperate. With a difficiently long number of cycles this strategy marginally outperforms a naive Tit-for-Tat strategy.

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 "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.

External link

• Wired magazine story about Tit for Tat finally being defeated

References

• The Evolution of Cooperation, Robert Axelrod
• The Origins Of Virtue, Matt Ridley, Penguin Books Ltd, ISBN 0140244042