Green construction is considered to be a construction model that pursues high resource efficiency and the utilization of reduced environmental impacts through technological innovation and management optimization under the realization of the project’s iron triangle. The realization of its performance relies on the level of stakeholder capability configuration. To reveal the optimal capability configuration and interaction between regulators and executors, this study constructed a utility model based on a post-positivist methodology. By analyzing the optimal capability configuration and coordination levels of regulators and executors according to the practices and constraints of green construction, this study conducted a static analysis to compare the effects of marginal value on regulators’ capability input and coordination coefficients. Finally, a sensitivity analysis uncovers the changes in capability configuration interaction and coordination coefficients at different stages of green construction. The results indicate that high levels of coordination in green construction cannot be maintained in the long term; continuous capability input from regulators is required for sustained support. Only by eliminating external uncertainties, reducing the variable costs for executors in advancing green construction, and controlling their risk aversion can executors be truly motivated to promote green construction. The capability configuration of both regulators and executors adjusts with corresponding marginal values. The capability configuration of executors shows a trend of initially increasing and then decreasing as the progressive coefficient rises. The model proposed in this study ensures that the final coordination level stabilizes at a relatively high level, which is between 0.6 and 0.7. In summary, the breakthrough findings provide critical insights into green construction management, contributing to the achievement of the anticipated green construction objectives.