The complementary roles of conformity and Q-learning in the prisoner's dilemma with punishment.

Punishment has been demonstrated to be an effective mechanism for promoting cooperation, both theoretically and experimentally. However, most previous studies have focused on a single update rule, which fails to reflect the diversity of real societies arising from cognitive heterogeneity. Therefore, this paper investigates the evolutionary dynamics of the prisoner's dilemma with punishment by incorporating Q-learning and conformity update rules. These two rules capture two typical types of individuals commonly observed in real societies: profit-seeking explorers and conservative conformists. We show that an appropriate mixture of the two update rules promotes cooperation through complementary roles: conformity forms clusters to protect cooperation, while Q-learning drives cooperators' expansion with the help of punishment. This complementarity weakens when conformists dominate. Moreover, we demonstrate that our results are robust across different network structures and punishment parameters. Our findings demonstrate that an appropriate mixture of Q-learning and conformity update rules maximizes the effectiveness of punishment in promoting cooperation.