Because of the cross-domain status of labor, a characteristic of mobility is often added to individual occupational safety and health. Cooperative governance of occupational safety and health is a key issue and a difficult problem for the government. Based on health footprint perspective, evolutionary game method and numerical simulation were employed to analyze the behavioral evolutionary path and stabilization strategies employed by government for the management of occupational safety and health issues. The findings show that with respect to the governance of occupational safety and health issues, local governments that lack constraints are likely to fall into the “prisoner’s dilemma” of occupational safety and health decisions. Further analysis shows that regulation and control by central government can rapidly promote cooperative government alliances among local governments. By evaluating a form of inter-governmental occupational safety and health governance that adopts the concept of health footprint, this study presents a new model of health governance and highlights the novel possibility of developing an inter-governmental alliance for cooperative governance.