  One of the most important questions in game theory concerns how mutual
cooperation can be achieved and maintained in a social dilemma. In Axelrod's
tournaments of the iterated prisoner's dilemma, Tit-for-Tat (TFT) demonstrated
the role of reciprocity in the emergence of cooperation. However, the stability
of TFT does not hold in the presence of implementation error, and a TFT
population is prone to neutral drift to unconditional cooperation, which
eventually invites defectors. We argue that a combination of TFT and anti-TFT
(ATFT) overcomes these difficulties in a noisy environment, provided that ATFT
is defined as choosing the opposite to the opponent's last move. According to
this TFT-ATFT strategy, a player normally uses TFT; turns to ATFT upon
recognizing his or her own error; returns to TFT either when mutual cooperation
is recovered or when the opponent unilaterally defects twice in a row. The
proposed strategy provides simple and deterministic behavioral rules for
correcting implementation error in a way that cannot be exploited by the
opponent, and suppresses the neutral drift to unconditional cooperation.
