Abstract: Under the "dual carbon" goals context, examining the evolutionary game relationship between the government and enterprises within the green financial market using game theory holds significant implications for advancing the green transformation of the macroeconomy. This study employs a phase diagram analysis within the game decision-making theoretical framework and utilizes MATLAB software for empirical analysis. Numerical simulations were conducted to model the dynamic game process between the government and enterprises under green financial support. The research demonstrates that:(1)Within the bilateral regulatory game formed by the government and enterprises under green financial support, the decisions of both players exhibit mutual influence.(2)The government formulates green policies by referencing the statistics on penalized enterprises, while the net revenue of green projects is contingent on their social benefits.(3)Enterprises chosen green innovation strategies are significantly influenced by parameters related to their own profitability and the level of governmental green financial support. The findings provide valuable insights for incentivizing enterprises to pursue green innovation, establishing a dual-agent coordination mechanism within the green financial market system, and forming an effective interactive game framework between the government and enterprises.

Key words: game theory, green finance, green innovation