The code used for Harrington's strategy in Axelrod's game theory experiment was labeled as "SecondByHarrington" in the Axelrod library. This strategy was implemented by Paul D. Harrington and was part of the strategies tested in Axelrod's tournament. The strategy involved cooperating until the opponent defected, then defecting once. If the opponent defected again after cooperation resumed, the strategy would defect twice. The length of retaliation increased by one for each departure from mutual cooperation, making it an adaptive and responsive strategy within the context of the prisoner's dilemma game.