Who would rescue the dilemma of Chinese elderly care? An evolutionary game analysis and simulation research on the formalization of the domestic service industry with subsidy policy.

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.