A study of factors in the formation of population game cooperation based on mixed learning rules

In our population game model, we introduce an innovative concept: we assume that players possess both social imitation learning and personal history learning abilities. This mixed learning rule combines aspects of social and historical learning, offering a fresh perspective on strategy updates for cooperative evolution. To simulate player learning, we treat each player as a particle, and we propose a novel swarm intelligence algorithm in conjunction with the particle swarm optimization algorithm. We conduct simulations for three typical games using both random matching and square network models. The experimental results demonstrate that the mixed learning rule effectively overcomes the tragic Nash equilibrium observed in the Prisoner’s Dilemma game. It leads to the establishment of a stable proportion of cooperators, boosts the proportion of Hawk-Dove game cooperators, and enables coordinated game cooperators to dominate the entire population. Furthermore, our sensitivity analysis of the introspection rate and trade-off coefficient reveals that increasing the trade-off coefficient effectively enhances the average proportion of cooperators, while raising the introspection rate suppresses cooperation levels.