Balancing quality collaborative supervision and tripartite satisfaction in elderly healthcare public-private partnerships: an evolutionary game and simulation analysis

China’s rapidly growing elderly population, shifting social patterns, and economic developments have significantly impacted traditional family-based caregiving, leading to the widespread adoption of Public-Private Partnership (PPP) models for institutional care. Effective elderly care PPPs require quality collaborative supervision among the government, the private sector, and the public to ensure tripartite satisfaction and promote social well-being. However,challenges such as service quality failures and disputes in several regional elderly care PPP projects stem from insufficient government supervision and limited public participation, leading to information asymmetry, incomplete contracts, and suboptimal service quality. Existing research lacks comprehensive models that address the public’s role as a key stakeholder and the dynamic interplay among critical variables affecting PPP stability. This study uses evolutionary game theory (EGT) to explore the strategic interactions between the government, private sector, and public in elderly care PPPs. The model incorporates key factors such as reputation, damage compensation, and government intervention to enhance public participation and tripartite satisfaction. Findings reveal that (1) high-quality services, active public participation, and efficient government supervision are crucial for effective collaborative supervision. (2) Stakeholders’ initial willingness to cooperate, compensation for public interest damages, reputation, and punitive measures are key determinants for stability. (3) Compensation for public interest damages and guaranteed incomes significantly enhance public participation in the supervision process. MATLAB simulations validate the model’s stability, specifically, the simulation shows that the system evolves effectively toward the ideal state when public damage compensation exceeds participation costs and penalties for low-quality services outweigh the cost savings from providing them. Based on these findings, we propose targeted strategic measures such as calibrating compensation and penalty levels based on these threshold relationships to improve collaborative quality and ensure satisfaction among all stakeholders in elderly healthcare PPPs in China, with broader applicability to other sectors and regions.