In the contemporary era of increasing population aging, improving the service quality of senior care institutions and optimizing the regulatory behavior of multiple subjects has become a hot topic in society nowadays. Based on the welfare plurality theory and Li Yapunov theory, this paper analyzes the behavior of the government, senior care institutions, and the elderly in the regulation of senior care institutions, establishes a game model for the regulation of senior care institutions, and analyzes the mutual influence of the behavior of the multiple subjects in the regulation of senior care institutions by using the evolutionary game method. The results show that the service quality of senior care institutions is affected by many aspects, and with time, the rate at which senior care institutions, the government and the elderly converge to the equilibrium strategy becomes smaller and smaller, and the system will eventually reach a stable state at (1,1,1) (i.e., active government supervision, self-regulation of senior care institutions, and supervision of the elderly), and the government has a certain role in leading the optimization of senior care institutions’ supervision behaviors. This study has practical value for improving the quality of services offered by senior care institutions, meeting the senior care needs of elderly individuals, and enhancing collaborative governance among multiple stakeholders.