For whom is it more beneficial to stop interactions with defectors: Cooperators or defectors?

Cooperation is a mysterious evolutionary phenomenon and its mechanisms require elucidation. When cooperators can stop interactions with defectors, the evolution of cooperation becomes possible; this is one mechanism that facilitates the evolution of cooperation. Here, stopping interactions with defectors is beneficial not only for cooperators but also for defectors. The question then arises, for whom is stopping interactions with defectors more beneficial: cooperators or defectors? By utilizing evolutionary game theory, I addressed this question using a two-player game involving four strategies: (1) cooperators who stop the interaction if the current partner is a defector, (2) cooperators who attempt to maintain a relationship with anyone, (3) defectors who stop the interaction if the current partner is a defector, and (4) defectors who attempt to maintain a relationship with anyone. Our results show that, at equilibrium, the ratio of cooperators who stop the interaction if the current partner is a defector to cooperators who attempt to maintain a relationship with anyone is larger than the ratio of defectors who stop the interaction if the current partner is a defector to defectors who attempt to maintain a relationship with anyone. Thus, cooperators rather than defectors are more likely to stop interactions with defectors at equilibrium. This result is consistent with a previous experimental study in which a positive correlation was detected between the degree of individuals' cooperativeness and how accurately the individuals recognize whether other individuals are cooperators or defectors. Thus, the theoretical work presented in this study provides relevant insights into the natural phenomena of cooperation and recognition.