The sharing economy, which is characterized by the sharing of the right to use, has upset the balance of the original economic system, changed the original transaction mode and changed the decision-making behavior of the participants. For analysising the impact of the behavioral decisions of participants (i.e., platforms, owners and sharers) on the stability of the sharing economic system, an evolutionary game model composed of three game parties of "platform-owner-sharer" is established based on the assumptions of the network externality of platforms, the interaction of participants' behavior and bounded rationality. The asymptotic stability of equilibrium points and the evolutionary stability strategy of the system are analyzed by using evolutionary game theory and Lyapunov diagnostic method. Finally, the influence of network externality, opportunistic cost of participants and platform supervision on the stability of the dynamic system is explored, which provides a theoretical reference for participants' decision-making.