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In this study, we constructed a tripartite evolutionary game model for a large-scale enterprise (A), a small-scale enterprise (B), and a government, based on finite rationality and information asymmetry. First, we investigated and analyzed the stakeholders of low-carbon technology innovation (LCTI) and constructed a tripartite evolutionary game model. Then, we analyzed the conditions for the stability of different equilibrium points. Finally, we carried out numerical simulations using MATLAB 2020b to analyze the evolutionary processes and patterns of the different parameters. We found that the government’s strategic choice is always to participate in LCTI, which is conducive to a healthy LCTI environment. Governments can participate in LCTI consortiums through policy-driven reward and punishment mechanisms. Our simulation demonstrated that the size of enterprises influences their choice of LCTI strategy, and government reward and punishment mechanisms influence both large and small firms. Large firms are more prepared to accept the risks of LCTI and maintain a reciprocal LCTI strategy even in a high-cost scenario, while small firms are more sensitive to the costs and benefits. Thus, government reward and punishment mechanisms should take full account of small-scale enterprises. We propose a sound reward and punishment mechanism for LCTI that limits the opportunistic behavior of enterprises. Therefore, this paper is a complement to theories such as innovation systems and provides new thinking for low-carbon technology innovation cooperation of enterprises. Meanwhile, the reward and punishment mechanism proposed in this paper has important practical value for the government.