Evolution of cooperation in social dilemma games with continuous opinions based on the HK model

In real life, individuals hold diverse opinions on various issues, which influence their behavior and gradually shape their behavioral norms over time, thereby impacting group behavior. To explore how group behavior evolves under the influence of individual opinions, we introduce continuous opinions representing cooperation willingness into three social dilemma games. The Hegselmann-Krause (HK) model, which accounts for payoffs, is used for opinion updating to examine the effects of bounded confidence and the payoff enhancement factor on group cooperation. Numerical simulation results indicate that relatively small bounded confidence positively facilitates opinion convergence and group cooperative behavior, although the extent of facilitation varies slightly across the three different game models. It is only when the bounded confidence is relatively large that changes in the payoff enhancement factor have a significant impact on group cooperation. At this stage, a larger payoff enhancement factor fosters group cooperation in the stag hunt game, while its effects on the other two models are relatively modest.