Indirect reciprocity norms and cooperation in populations with PSO-based strategy update

Abstract This study investigates the evolutionary dynamics of strategies and cooperative behaviours in populations by incorporating different indirect reciprocity norms into the prisoner's dilemma framework. In these populations, agents base their cooperative decisions on trust shaped by social norms and update their strategies using a particle swarm optimization (PSO) rule. Through extensive computational experiments, we identify the ‘friend's friend is a friend, friend's enemy is an enemy, enemy's friend is a friend, and enemy's enemy is a friend' (RA) norm as the most effective indirect reciprocity norm for promoting cooperation and curbing the spread of defection. Moreover, we find that agents' preference for imitating the historically most successful strategy further strengthens the dominance of the RA norm, thereby facilitating the emergence of cooperation and the formation of cohesive community structures. Finally, our analysis reveals that population size and the number of interaction rounds exert only minor influence, whereas lower tolerance for defection and higher returns to cooperation is beneficial for promoting cooperative behaviour.