Evolution analysis of low-carbon cooperation of service providers based on Moran process in cloud manufacturing.

Low-carbon cooperation among cloud manufacturing service providers is one way to achieve carbon peak and neutrality. Such cooperation is related to the benefits to service providers adopting low-carbon strategies and stochastic factors such as government low-carbon policies, providers' environmental awareness, and demanders' low-carbon preferences. Focusing on the evolutionary process of service providers' low-carbon strategy selection under uncertain factors, a stochastic evolutionary game model is constructed based on the Moran process, and the equilibrium conditions for low-carbon cooperation among providers are analyzed under benefit-dominated and stochastic factor-dominated situations. Through numerical simulation, the effects of the cloud platform's cost-sharing coefficient for low-carbon investment, matching growth rate, carbon trading price, and group size on providers' low-carbon strategy evolution are analyzed. The research results show that increasing the cloud platform's low-carbon cost-sharing, carbon trading price, and group size can promote low-carbon cooperation among service providers. With greater low-carbon investment costs and greater stochastic factor interference, the providers' enthusiasm for low-carbon cooperation decreases. This study fills the research gap in the low-carbon cooperation evolution of cloud manufacturing providers based on the stochastic evolutionary game and provides decision-making suggestions for governments and cloud platforms to encourage provider participation in low-carbon cooperation and for providers to adopt low-carbon strategies.