Abstract: Under the background of an aging population, the elderly have overlapping demands for community medical services and old-age care services, but there is an imbalance of interests on the supply-demand side, resulting in insufficient effective supply of community medical and old-age care services. In order to relieve the pressure of pension for aging, based on stakeholder theory, in the construction of local government - community - a combined with institutions based on static game, the three of the elderly into the structure of dynamic supervision game model, clarify the relationship between the three interests and behavior, and evolutionary game model is analyzed using lyapunov criterion asymptotic stability of the equilibrium. The research shows that the introduction of dynamic supervision can better restrain the behavioral strategy fluctuation of stakeholders and make the compliance operation of community medical and nursing institutions the optimal choice. At the same time, local governments provide appropriate financial subsidies to community medical and nursing institutions and community elderly groups, so as to ensure fair and reasonable distribution of benefits among various subjects.

Key words: stakeholder; community; combination of medical care and nursing services