Combination with anti-tit-for-tat remedies problems of tit-for-tat

TL;DR

This paper proposes a combined strategy of Tit-for-Tat and anti-Tit-for-Tat to improve cooperation stability in noisy environments of the iterated prisoner's dilemma, addressing errors and preventing exploitation.

Contribution

It introduces a novel TFT-ATFT strategy that corrects errors and maintains cooperation without being exploitable, enhancing the robustness of reciprocity-based strategies.

Findings

TFT-ATFT effectively corrects implementation errors.

The strategy prevents neutral drift to unconditional cooperation.

It maintains stable cooperation in noisy environments.

Abstract

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.