Optimizing the home-school-society collaborative mechanism for college students' mental health: an evolutionary game theory approach

The mental well-being of college students is a critical concern that requires a collaborative effort from families, schools, and society. However, the internal mechanisms and key factors that drive effective collaboration among these three parties remain unclear, hindering the establishment of a robust support system.This study constructs a tripartite evolutionary game theory model involving families, schools, and societal institutions. The model investigates the impact of government policy support (including financial subsidies), cost-sharing arrangements, and benefit allocation mechanisms on the behavioral strategies of all stakeholders. Stability analysis and numerical simulations were employed to examine the dynamic evolution of the system.The simulation results indicate that targeted government subsidies significantly enhance the participation enthusiasm and sustained engagement of families and schools. Furthermore, the incentive intensity for social institutions is a pivotal factor in promoting their willingness to open and share resources. A stable, high-collaboration state can be achieved when families receive sufficient policy support, schools' coordination costs are covered, and the benefits for social institutions exceed their input costs. The findings confirm that an optimized incentive structure is essential for sustainable collaboration. This paper concludes by proposing concrete policy recommendations to improve the long-term home-school-society collaborative mechanism for college students' mental health, offering a valuable theoretical and practical framework for stakeholders.