Abstract: Since its implementation in 2009, China's hierarchical medical system has faced the dilemma of structural resource imbalance: Grade 3A hospitals (China’s highest-ranked medical facilities), accounting for only 7.6% of the total number of hospitals, bear nearly 50% of the patient visits, operating under prolonged high load; while the utilization rate of primary medical institutions （such as community hospitals） remains below 60%. Due to information asymmetry and a lack of trust in community hospitals, patients with minor illnesses flock to Grade 3A hospitals, exacerbating the issues of "difficult and expensive access to healthcare". Internet of Things (IoT) technology offers a new pathway to optimize medical resource allocation and enhance the efficiency of hierarchical diagnosis and treatment. However, its investment decisions require systematic analysis of the interactive effects of patient behavior choices, hospital competitive strategies, and policy constraints. The core problem addressed in this paper is: Within a two-level referral system consisting of Grade 3A hospitals and community hospitals, how can IoT investment by community hospitals alter patient choice of healthcare providers, alleviate congestion in Grade 3A hospitals, and simultaneously optimize the pricing strategy of Grade 3A hospitals to achieve the goals of hierarchical medical care. This paper solves the problem by constructing a three-stage dynamic Stackelberg game model, where the Grade 3A hospital acts as the leader, the community hospital acts as the follower, and patient choice is respected. M/M/s queuing theory is employed to quantify waiting costs and characterize service congestion effects. The problem-solving approach is as follows: 1.Patient Diversion Mechanism: Community hospitals invest in IoT to enhance perceived service value, reducing the proportion of patients choosing Grade 3A hospitals. A threshold effect in the diversion mechanism is discovered: Diversion is only effective when the service capacity of the community hospital exceeds the residual capacity of the Grade 3A hospital (μ_C>C_A), and the IoT investment level(β) is sufficiently high. 2. Grade 3A hospital Pricing Response: When the community hospital's IoT investment level(β) is high, the Grade 3A hospital needs to lower its price(p) to retain patients. A government-guided price ceiling(p ̅=U-h/(μ_A-Λ)) constrains the maximum price, preventing monopolistic premiums. 3. Game Equilibrium of IoT Investment and Pricing: The community hospital's optimal IoT investment level depends on the Grade 3A hospital's price(p) and its own service capacity(μ_C). The Grade 3A hospital dynamically adjusts p based on (μ_C): If μ_C is low, it maintains a high price(p^*=p ̅); if μ_C is high, it balances between the profit-maximizing point(p_0)and p ̅. Key Findings: IoT Investment Diversion Effect: When β is sufficiently high (β^*=θU/(z+P)-1), α (proportion choosing Grade 3A hospital) decreases significantly, shifting patients with minor illnesses to community hospitals. The critical condition μ_C>C_A is a necessary condition for successful diversion (otherwise all patients flow to the Grade 3A hospital). 2. Grade 3A hospital Pricing Strategy: High community hospital capacity (μ_C>λ_C+M) forces the Grade 3A hospital to lower its price(p). The government-guided price(p ̅) effectively suppresses "expensive healthcare". 3. System-Level Benefits: Alleviates "difficult healthcare": High β reduces queuing congestion in Grade 3A hospitals (waiting cost h/(μ_A-λ_A-αλ_C ) decreases). Reduces "expensive healthcare": Competitive pressure lowers the Grade 3A hospital's price(p), and community hospitals offer near-free services. Achieves Hierarchical Care: IoT supports information sharing and a two-way referral system, optimizing resource matching. Conclusion The IoT investment level of community hospitals is a key lever for the success of hierarchical medical care: When investment is high, it creates a virtuous cycle of "patient diversion → Grade 3A hospital price reduction → decrease in both cost and waiting". Conversely, the hierarchical system fails. The government needs to constrain Grade 3A hospital pricing via guided prices and incentivize IoT construction in community hospitals. Future research could explore cross-hospital cost-sharing mechanisms and empirical validation.

Key words: Medical Behavior Choice, Tiered Health Care System, IoT, Queuing Theory, Dynamic Game