Since China entered the aging society, the surging demand for elderly care and the industrial upgrading of “silver economy” has forced the domestic service industry to face endogenous challenges. Among them, the formalization of the domestic service industry can effectively reduce the transaction costs and risks of actors, innovate the endogenous vitality of the industry, and promote the improvement of elderly care quality through a triangular employment relationship. By constructing a tripartite asymmetric evolutionary game model of clients, domestic enterprises and governmental departments, this study uses the stability theorem of differential equations to explore the influencing factors and action paths of the system's evolutionary stable strategies (ESS), and uses the research data collected from China to assign values to models for simulation analysis. This study finds that the ratio of the initial ideal strategy, the difference between profits and costs, subsidies to clients, and subsidies or punishments for breach of contract to domestic enterprises are the key factors affecting the formalization of the domestic service industry. Subsidy policy programs can be divided into long-term and periodic programs, and there are differences in the influence paths and effects of the key factors in different situations. Increasing domestic enterprises' market share with employee management systems, formulating subsidy programs for clients, and setting up evaluation and supervision mechanisms are efficient ways through which to promote the formalization of the domestic service industry in China. Subsidy policy of governmental departments should focus on improving the professional skills and quality of elderly care domestic workers, and also encourage domestic enterprises with employee management systems at the same time, to expand the scope of service beneficiaries by running nutrition restaurants in communities, cooperating with elderly care institutions, etc.