Cooperation evolution in spatial public goods games with dynamic morality and third-party supervision

Understanding how external institutions and internal morality synergize to manage the evolution of cooperation remains a central challenge in social dilemmas. To address this problem, we integrate dynamic moral preferences with third-party supervision into the spatial public goods game. Individuals update moral scores based on their behavior and the strategies of their neighbors, while supervisors reward or punish according to local cooperation and moral scores, with a supervision cost incorporated when reward or punishment is triggered. Extensive Monte Carlo simulations show that moral learning accelerates the spread of cooperation, while supervision primarily restricts defection. In particular, a moderate incentive threshold (β) combined with a relatively fast moral adaptation rate (α) creates a marked synergistic effect, enabling the group to achieve and maintain near-full cooperation. Further results indicate that supervision cost weakens the net incentive effect of third-party intervention, but cooperation can still be maintained under favorable enhancement factors and appropriate supervision intervals. This synergy is manifested in the significant expansion of the parameter region that supports stable cooperation and the rapid formation of robust cooperative clusters. Our findings highlight the effectiveness and limitations of a dual-driver governance framework integrating institutional and moral mechanisms, offering theoretical insights into the complex interactions between institutional norms and moral behavior in society.