Intergovernmental collaboration is essential for regionally coordinated air pollution prevention and control. An evolutionary game model of local government behavior strategy selection taking into account the fixed cost of the local government, the total amount of network production factors, and the total amount of total network factors of production that can be moved is built based on the social capital theory in order to realize the cross-border collaborative control of regional air pollution. The issue of an intergovernmental cooperation framework for collaborative prevention and control of large-scale air pollution is addressed from the standpoint of the multi-stakeholder “benefit–cost” drive. Additionally, the major variables influencing the behavioral approach selection for intergovernmental cooperation are considered. The initial sensitivity of the evolution path of the local government behavioral strategy is also analyzed. The results of this study are: (1) The primary elements impacting intergovernmental cooperation on joint prevention and control of air pollution are fixed costs and fixed benefits, and reducing the fixed costs of such cooperation in an appropriate manner without compromising local governments’ pollution control can do so. (2) Under the assumption that local governments have fixed expenses, the total amount of network factors of production and total network factors of production that can be moved factors of production have a direct impact on intergovernmental cooperation. When local governments’ fixed costs are constant, they are more likely to choose the cooperative behavior option if the sum of their network production factors and total network factors of production that can be moved is higher. (3) The initial probability of cooperation among the three parties and the total amount of production factors have an impact on the system’s ESS when local governments in the area have equal total production factors. The study’s findings can offer theoretical justification for the “profit-driven” intergovernmental coordination of joint prevention and management of air pollution.