Abstract: In the internet era, online media has become an important carrier of rumors spreading, which seriously threatens the safety and social harmony and stability of China's network space. Compared with traditional media, online media has become an important force for informational dissemination in emergencies, with its characteristics of large users, fast informational dissemination, and strong interactive function. Facing the complex network environment, what is the evolutionary equilibrium strategy of the local government and online media after repeated games? What are the key factors affecting the choice of local government and online media to respond to online public opinion strategies? How to realize the co-ordination of local governments and online media to cope with sudden crisis events by adjusting the central government punishment mechanism? These new problems are worth studying.
In this paper, considering the bounded rationality and information asymmetry of game subject, the evolutionary game theory is used to construct the evolutionary game model between the network media and the local government supervision department. Based on the introduction of the central government punishment mechanism, discussing the governance model of online public opinion,which is dominated by local government regulatory authorities and actively responded by online media.
Firstly, constructing an evolutionary game model of local government and online media in response to the behavioral strategy of sudden crisis events, and solving the evolutionary conditions of the network's public opinion heat propagation system to the local stable equilibrium state. Secondly, in order to make the system evolve to a rational state, the central government punishment mechanism is included in the above evolutionary game model. Establishing an extended evolutionary game model in which local governments and online media collaborate to manage network sentiment in sudden crisis events and derive the optimal evolution strategy of behavioral strategy choices between local governments and online media. Finally, the different types of sudden crisis are selected as research cases, and multiple scenarios are derived from the behavioral strategies of online media and local governments. The evolution and stability of the behavior strategies of the two parties under different scenarios are compared and analyzed.
The results of the study show that the public sentimental heat of sudden crisis events has a direct relationship with the choice of online media and local regulatory authorities. When the local government regulatory authorities are exposed to sudden crisis events, the economic losses and reputation losses caused by the vicious evolution of the network are constantly increasing, and the evolutionary systems of both sides will experience cyclical fluctuations. After the introduction of the central government punishment mechanism, if the punishment is higher than the punishment of the online media negatively responding to the Internet public opinion and the supervision input cost of the local government supervision department, and the system will ultimately evolve to a balance state.
The conclusion of the study is providing a new idea for government departments to solve the network public opinion in sudden crisis.

Key words: sudden crisis, online public opinion, government management, evolutionary game, scenario analysis