Dynamic Pricing and Subsidy Strategies in Public Service Platforms with Private Participation: A Two-Level Stackelberg Game Approach

(1) Background: Public service platforms (PSPs) have become increasingly popular for delivering public services. Typically, their fixed pricing and subsidy strategies overlook the participation of various stakeholders, resulting in inefficient supply of public services. This study aims to use China’s eldercare services as an example to examine its dynamic pricing and subsidy strategies. (2) Methods: Game theory was utilized to develop a two-level Stackelberg game framework considering the decision-making sequences among stakeholders with competing objectives. On this basis, the two-level Stackelberg game was solved based on the maximization of social welfare, platform profit, and utility, pursued by the government, private sector, and service providers, respectively. (3) Results: The service supply duration is determined by the service price. Specifically, when the service price falls within an appropriate range, the optimal supply duration increases with the service price. The results further show that the optimal service price increases with the platform’s commission rate but declines with government subsidies. Furthermore, the optimal government subsidy increases with the platform’s commission rate in a balanced market. By contrast, in an unbalanced market, where demand is either below the minimum supply or above the maximum supply, the government will withdraw subsidies entirely once the commission rate exceeds a certain threshold, thereby curbing excessive commission charges. (4) Conclusions: This study contributes to the body of knowledge of platform development by examining PSPs’ dynamic pricing and government subsidy strategies. Practically, this two-level Stackelberg game framework for PSPs will help improve the efficiency of public services provision for consumers and maximize social welfare and platforms’ profit for the government and private sector, respectively.