In this article, we construct a game model that uses government regulators and scrap vehicle owners as the main parties to investigate the carbon credit exchange strategy of scrap vehicles using evolutionary game theory. The results were validated using Matlab simulation analysis to reveal the dynamic evolution process of the strategy of both sides of the game. A sensitivity analysis of the key parameters was conducted to explore the influence of each parameter on the evolution process and the stabilization trends. The study shows that (1) The time for the game system to reach a steady state is inversely related to the size of the initial willingness of the parties to cooperate. (2) In the mixed steady-state scenario, when the overall return differential between the positive and negative regulatory verification by government departments is positive, the steady state is participation and positive scrapping. (3) When the probability of the government verifying and being successful in verifying the punishment of the owner's negative scrapping behavior increases, both parties of the game will eventually choose the strategy of participation and positive scrapping. When the cost of the government participation strategy and the cost of the government verification strategy increase, both sides of the game will eventually choose the strategy combination of no participation and positive scrapping. (4) When the owner's reward for cooperating with the strategy, the owner's cost of scrapping the vehicle, and the benefits of the owner's negative cooperation strategy change, they will not change the strategy stability results but will affect the time it takes for the game system to reach a stable state. This study has theoretical implications for government policies in the scrapping industry and how to guide vehicle owners to actively scrap their vehicles.