Study of purchasing behavior evolution of work-safety-service based on hierarchical mixed supervision

This paper explores the evolutionary rules of work-safety-service purchasing strategies of enterprises under hierarchical mixed supervision. Considering the influence of the central government's inspection on local governments, an evolutionary game model is built which depicts the mutual interactions of work-safety-service purchasing strategies from enterprises and supervision strategies from local governments. The existence and stability of system equilibrium points are analyzed, and the influence of different parameters' variation on the evolutionary results is demonstrated through numerical simulation. It is found that different ranges of parameters affect the number and stability of equilibrium points and the evolutionary trend. The system converges to two different patterns. In the first pattern, local governments choose to supervise enterprises strictly and enterprises choose to purchase work-safety service, which is a desired pattern. In the second pattern, local governments choose to supervise enterprises loosely and enterprises choose not to purchase work-safety service, which is an undesired pattern. When it has five equilibrium points, it is feasible to make the system converge to the desired pattern through modifying relative parameters, avoiding the undesired pattern. The system is more likely to converge to the desired pattern with the higher initial ratio of local governments opting for strict enterprise supervision; the system is more likely to converge to the desired pattern when the central government exerts a stricter inspection on local governments; the system is more likely to converge to the desired pattern when local governments exert stricter ex ante and ex post safety supervision on enterprises. The system is more likely to converge to the undesired pattern when the ex ante supervision costs of local governments get higher. Subsidies from local governments for the purchase of work-safety service barely affect the evolutionary trend of the system.