Enhancing cooperation by balancing the contributions of early and late movers in spatial threshold public goods games

The challenge of public goods provision is amplified by the free-rider problem, particularly when late movers exploit the efforts of early contributors, disrupting efficiency and fairness. To tackle this issue, we propose an evolutionary public goods game model wherein the collective success relies on total contributions from both early and late movers reaching a critical threshold. Early movers decide independently based on anticipated payoffs, while late movers adaptively decide whether to cooperate or defect based on observed early contributions. A dynamic role transition mechanism, driven by payoff disparities, facilitates flexible shifts between early and late roles, encouraging adaptive decision-making. Our analysis indicates that late movers generally impede cooperation, especially under extreme parameter conditions. Sustainable cooperation emerges from a finely tuned parameter balance, ensuring adequate contributions from both groups. This framework extends evolutionary game theory by offering a nuanced perspective on cooperative strategies and practical recommendations for designing policy interventions to enhance collective outcomes.