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Contrary to what often seems to be accepted, 100% Tit-for-Tat is not an ESS, even in the three-pure-strategy game Tit-for-Tat-Always Cooperate-Always Defect, for which 100% Always Defect finally remains the only attractor for the composition of “asexual” populations. The present paper firstly investigates the dynamics of the Tit-for-Tat-Always Cooperate-Always Defect game for asexual populations, with the more realistic assumption that Tit-for-Tat sometimes fails to apply its algorithm. Surprisingly, this perturbation of the original game leads to different attractor patterns, in relation to the numerical values of the expected number of meetings and of Tit-for-Tat’s failure rate. These patterns generally include one punctual attractor for which most dyads at least partially cooperate. Nevertheless, the attractor alternative to 100% Always Defect in each pattern may become unstable when certain mixed strategies (cooperating and defecting at random) are introduced into the game, and the whole flow of strategy frequencies may then converge towards 100% Always Defect. Beyond the reiterated Prisoner’s Dilemma, the present analysis illustrates how self-organizing processes at infra-populational levels, like that occurring in dyads including at least one fallible Tit-for-Tat, can influence the evolution of populations.