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.

Example of Play

Assume there are four agents: two are Tit for Tat players ("variables") and two are simply trying to maximize their own winnings ("controls"). Assume that each player faces the other three in a match lasting six games. If one player gives evidence against a player who does not, the former gains five points and the latter nets zero. If both refrain from giving evidence, both gain three points. If both give evidence against each other, both gain one point.

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When a variable faces off against a control, the former refrains from giving evidence in the first game while the control does the opposite, gaining the control five points. In the remaining five games, both players give evidence against each other, netting one point each game. The final score is control, ten; variable, five.

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When the variables face off against each other, each refrains from giving evidence in all six games. Six times three is eighteen points for each variable.

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When the controls face off, each gives evidence against the other in all six games. Six times one is six points for both controls.

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The final score for each variable is five plus five plus eighteen, or twenty-eight points. The final score for each control is ten plus ten plus six, or twenty-six points. Despite the fact that the variables never won a match and the controls never lost a match, the variables still came out ahead, because the final score is not determined by the winner of matches, but the scorer of points. Simply put, the variables gained more points tying with each other than they lost to the controls.

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(This example was taken from Piers Anthony's novel, Golem in the Gears.)

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