This study examines the decision-making optimization of Power-Generation Enterprises (PGEs) in the green certificate market, with a focus on balancing bidding strategies and carbon-reduction targets. Given the increasing complexity of the green certificate market, the research employs Bayesian games, evolutionary games, and Stackelberg games to systematically analyze the strategic behavior of PGEs and their interactions within the market framework. The findings demonstrate that game theory facilitates cost structure optimization and enhances adaptability to market dynamics under policy-driven incentives and penalties. Additionally, the study explores the integration of stochastic modeling and machine learning techniques to address market uncertainties. These results provide theoretical support for policymakers in designing efficient green electricity market regulations and offer strategic insights for PGEs aligning with carbon neutrality objectives. This work bridges theoretical modeling and practical application, contributing to the advancement of sustainable energy policies and the development of green electricity markets.