Population aging poses challenges to the immature elderly care service system in many countries. The strategic behaviors of different participants in the provision of elderly care services in a long-term and dynamic situation have not been well studied. In this paper, an evolutionary game model is developed to analyze the strategic behaviors of two types of participants—the government sectors and the private sectors in provision of elderly care services. Firstly, eight scenarios are analyzed, and the evolutionary process and stable strategies are identified. Then, the behavioral strategies of the two types of participants under demand disturbance and dynamic subsidy strategy are analyzed. Simulation experiments are conducted to explore the influence of different initial conditions and parameter changes on the evolutionary process and results. The obtained observations are not only conducive to a systematic understanding of the long-term dynamic provision of elderly care services but also to the policymaking of the government.
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