How much cost should reciprocators pay in order to distinguish the opponent's cooperation from the opponent's defection?

Reciprocity is a potential mechanism that encourages the evolution of cooperation. We consider the case where reciprocators' cognitive ability of distinguishing the opponent's cooperation from the opponent's defection imposes a recognition cost. While it is natural to consider how recognition accuracy depends upon the magnitude of the recognition cost, it is rather unclear which amounts of the recognition cost paid by the reciprocator are most likely to evolve. By using the evolutionarily stable strategy analysis, we herein tackle this problem and show that the condition under which reciprocators can resist the invasion of unconditional defectors is most relaxed when they have perfect perception. We further consider a game with three strategies played by unconditional defectors and two types of heterogeneous reciprocators with different perceptual abilities. Our analysis shows that only when execution error rates are large enough, it is possible for reciprocators with lower perceptual ability to resist the invasion of both the unconditional defectors and reciprocators with higher perceptual abilities. These findings advance our understanding of the evolution of perception and its eminent role in the evolution of cooperative behavior.