Optimal carbon–neutral strategies in the healthcare system: A three-stage Stackelberg game model

The healthcare sector is a major contributor to global carbon emissions, accounting for approximately 4%–5% of greenhouse gases. Despite growing concerns about environmental impacts, existing research largely isolates carbon reduction strategies specific to certain medical processes or supply chain components, neglecting the integrated nature of decision-making among key healthcare stakeholders. This paper bridges this gap by developing a comprehensive decision framework for optimal carbon–neutral strategies within a four-tier healthcare system comprising the government, non-profit hospitals, for-profit hospitals, and patients. Government carbon policies significantly influence hospital investments in carbon–neutral operations, which subsequently affect patient choices based on pricing and service quality. To optimize this process, a three-stage Stackelberg game model is formulated that captures the hierarchical and interdependent decision-making processes characteristic of healthcare operations. An incorporated algorithm consisting of four sub-algorithms is proposed, combining two methods: (1) discretization of medical service pricing and quality on hospital-level operations, and (2) a grey wolf optimizer-based heuristic method to determine optimal government policies regarding carbon tax, emission reduction subsidies, and carbon absorption subsidies. To verify the model and validate the algorithm, numerical experiments are conducted using data from a non-profit hospital in Canada and a for-profit hospital in the UK. This study introduces a novel, multi-tier decision model that links carbon policy governance with hospital operational decisions and patient behavior. The results provide practical insights for policymakers and hospital administrators, laying the groundwork for future empirical studies in sustainable healthcare management.