Dynamic Research on the Collaborative Governance in Urban and Rural Black-Odorous Water: A Tripartite Stochastic Evolutionary Game Perspective

The issue of black-odorous water (BOW) represents a formidable challenge to the current aquatic ecosystems, and its governance exhibits characteristics of low efficiency, susceptibility to relapse, and fragmented management under the Central Environmental Protection Inspection, thereby emerging as a dynamically complex issue in the ecological governance of urban and rural settings. This study introduces Gaussian white noise to simulate environmental uncertainty and design a stochastic evolutionary game model encompassing the central government, local governments, and societal forces based on evolutionary game theory and classical governance theories and concepts. Numerical simulations are conducted to explore trajectories of the strategic evolution of various subjects influenced by numerous factors. Results indicate that under the environment of random disturbances, the strategies of the game subjects show significant fluctuations, but actively cultivating the subject’s initial willingness facilitates collaboration governance in inspection. Moreover, joint construction of a “belief system” by multi-subjects, the intensity of inspection interventions, the integration of heterogeneous resources, and effective punitive measures all influence the governance of BOW, but the efficiency of resource allocation should be considered throughout the governance process. Recommendations are made finally for collaborative governance of urban and rural BOW, promoting the sustainable development of the ecological environment.