Abstract: In the process of carbon emission mitigation, as two major participants of emission mitigation, government and enterprise play crucial roles, and subsidy and punishment are two key methods of government. However, the objectives of government and enterprise are not consistent and there exists a game between these two participants in the implementation of carbon emission mitigation. It is critical to handle correctly the contradiction between the government and enterprises. Considering that evolutionary game theory is an effective method in the research of this contradiction, an evolutionary game model is constructed in this paper under the mechanism of static and dynamic subsidy or punishment by local government.Four Influencing paramenters, including carbon allowance, carbon trading price, goveornmental supervision fee and enterprice abatement invest (emission reduction effect paramenter), are compared for their contributions to the evolutionarily stable strategy. The results show that:(1)under the mechanism of dynmaic subsidy or punishment, the trajectory of evolutionary game, cycles around and approach spirally the only evolutionarily stable strategy, is less influenced by the original states of local governments and enterprises.(2)Both the governmental supervision fee and enterprice abatement investment have a negative effect on the action tactics of government supervision. (3)The the impact of carbon allowance on government is relate to the per unit of emission redcution market returns.(4)With the increase of governmental supervision fee, the level of honestly reducing emission will reduce.(5)As carbon trading prices rising, the positivity of government supervision increases initially and then decreases, the actions of enterprise carbon trading vary from buying to selling carbon emission rights, but the transition of the governmental supervision actions lag behind the change of enterprise carbon trading behavior. Furthermore, according to the request of model and the actual environment of carbon market in China, an analysis about all parameters' influence on evolutionarily stable strategy is made. The conclusions provide useful managerial implications for local governments to make policies, and enterprises to invest about reducing emission under the carbon trading mechanism.

Key words: the mechanism of subsidy or punishment, carbon emission constraints, evolutionary game, evolutionary stable strategy