The relationships within the carbon emissions game are diverse and intricate, encompassing both horizontal games between regions and vertical games involving governments, enterprises, and the public. To explore the complex game relationships among carbon emission entities, this study integrated horizontal and vertical games and applied the system dynamics method to construct a multilevel and multiagent cross-game model, analyzing the changing trends of strategies among different regional governments, enterprises, and the public. The research reveals that there is free-riding behavior in the governance of carbon emissions among regions. However, this free-riding behavior can lead to a virtuous cycle. The attitude of the government plays a crucial role in determining whether businesses engage in carbon emission management. Increasing government regulatory efficiency does not alter the outcome of the game, but it can reduce the time required to reach Nash equilibrium. The study enhances the simulation of carbon emission game theory and provides a reliable reference for government regulation and low-carbon development in businesses.