To effectively understand the collaborative and evolutionary mechanisms of three stakeholders in carbon trading namely, government, emission reduction enterprises, and emission control enterprises, it is important to identify the factors that affect decision-making behaviors amongst game players, ultimately contributing to the goal of “double carbon”. In this study, we constructed a tripartite game model, analyzing the selection mechanism for game strategies related to carbon trading participants through replicated dynamic equations. We also discussed the main factors that influence the evolutionary and stable outcomes of carbon trading through scenario simulations. Additionally, we introduced prospect theory to examine the impact of risk sensitivity and loss avoidance levels amongst decision-makers on the optimal outcome of the system. Our findings reveal that in the initial game model, the three decision-makers show a cyclical behavior pattern, but the system stabilizes in the optimal equilibrium state (1,1,1) when certain conditions are satisfied. Furthermore, the initial willingness of decision-makers impacts the ability of the game system to reach a stable point. Moreover, larger values for the risk sensitivity coefficient and loss avoidance coefficient can promote the evolution of the game system toward an optimal, stable point. Based on these results, targeted countermeasures are proposed to promote activity within the carbon trading market, such as giving more institutional guarantees to carbon trading and stabilizing the carbon price.