Due to the contradictions between environmental protection and the contemporary means of producing material-economic growth, companies are increasingly being placed on the Greenwashing List in China. The increasingly severe problem of greenwashing needs to be solved urgently. Government regulation plays a critical role in the prevention of greenwashing. Therefore, we introduce government regulation as a factor in the decision-making process of an enterprise's adoption of greenwashing, thus enriching the literature on the prevention of greenwashing and the validity of government regulations for green washing. Centered on heterogeneity, this paper divides enterprises into two types, i.e., dominant and inferior enterprises. In terms of game modeling, this study builds two evolutionary models that are influenced by a government punishment mechanism and tax subsidy mechanism for greenwashing and green innovation strategies and analyzes the evolutionarily stable strategy (ESS) of the models and the evolutionary process of dominant and inferior enterprises. This study found that the government punishment mechanism has an excellent inhibitory effect on the greenwashing practices of both dominant and inferior enterprises. However, the government tax subsidy mechanism is not able to suppress the greenwashing practices of inferior enterprises. In addition, the heterogeneities difference may determine whether green innovation strategies can be diffused and the speed of diffusion. As illustrated above, these results provide proposals for reducing the rate of greenwashing behaviors and for improving the effectiveness of the government regulation of companies' greenwashing behaviors. (C) 2019 Elsevier Ltd. All rights reserved.