Energy-intensive enterprises form the backbone of low-carbon transformation in our society, which is attracting significant attention in terms of government policy-making. However, existing studies focus largely on the behavior of governments or enterprises in emission reduction; what is not asked-and therefore not explained-is the coordination mechanism between government and industry. More crucially, very few studies have taken the initial willingness of both governments and enterprises into consideration. The absence of that research may lead to a certain amount of conflict between economic development and environmental protection by local governments, leading to looser regulation. Meanwhile, energy-intensive enterprises would perceive local gov-ernments as tending toward laxity, further negatively affecting emission reduction. To help fill in these gaps in the literature, we build an evolutionary game model consisting of energy-intensive enterprises and the government. Specifically, we first construct a revenue matrix including governments and energy-intensive enterprises, and then analyze their evolutionary stabilization strategies in four cases: strict regulation with carbon emissions, strict regulation without carbon emissions, loose regulation with carbon emissions, and loose regulation without carbon emissions. It should be noted that the model is built with consideration of penalties levied by higher-level governments for lax regulation by local governments. Likewise, in the initial game state, the probabilities of energy-intensive enterprises taking the initiative to reduce emissions and strict government regulation represent the initial intention the respective parties. Finally, the dynamic evolution process is simulated numerically. Our main findings are as follows. 1) Government regulations and costs of reducing emissions are determinants of the equilibrium state in the game model. In the case of loose regulations or high emission reduction costs, both governments and enterprises embrace strategies with a negative effect on emission reduction. 2) Without effective external constraint mechanisms, both the government and enterprises would make decisions to maximize their own benefits. Doing so would lead to a sub-optimal equilibrium, impeding the achievement of ideal emission reduction goals. 3) The initial willingness of governments and enterprises determines emission-reduction paths. Likewise, the initial intention to engage in strict regulation by governments exerts a stronger constraint on enterprises. Therefore, to guarantee policy efficiency, governments need to implement strict regulations, decrease enterprises' emission reduction costs, and enhance the initial willingness of both sides. Under these conditions, energy-intensive enterprises would be more likely to accomplish low-carbon transformation.
