Abstract：In order to explore the influencing factors of related subjects' strategic behavior under the background of joint reward and punishment of environmental credit, and considering public environmental attention, a three-party stochastic evolutionary game model of local government, third-party governance enterprise and polluting enterprise is constructed. The It＾o stochastic differential equation theory is used to analyze the conditions of game subject behavior stability while numerical simulation method is used to investigate the strategic evolution of the game subject. The results show that the positive pollution control strategy of third-party governance enterprise will drive polluting enterprise to choose environmental protection and trustworthy strategy, and their strategy choice will influence each other. Public environmental attention has promoting effect to the tripartite game subject strategy convergence. For the strategy of local government, the government at a higher level of penalties is of decisive role for its strategy choice. Rewards and punishments distribution ratio has the directional difference to third party governance and pollution enterprise strategy convergence, and reward incentive is more significant.
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