Tit for Tat

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 initially cooperate, then 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.

Overview

This strategy is dependent on four conditions that has allowed it to become the most prevalent strategy for the Prisoner's Dilemma:

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• 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.

In the last condition, the number 2/3 is arbitrary and 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.

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A fifth condition applies to make the competition meaningful: if an agent knows that the next play will be the last, it should naturally defect for a higher score. Similarly if it knows that the next two plays will be the last, it should defect twice, and so on. Therefore the number of competitions must not be known in advance to the agents.

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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).

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