In this study, to reduce the occurrence of risks and risk accidents in the construction stages of engineering projects and strengthen the risk management abilities of the subjects of such projects, prospect theory is introduced into an evolutionary game to construct a risk management behavior game model between owners and contractors in the construction stage. In addition, a government penalty parameter is introduced based on strong reciprocity theory. The intrinsic laws and optimal evolutionary stability strategy in the behavior evolution game between the two parties are analyzed. The influences of different parameter changes on the evolution results are simulated. The study shows that the game model has five local equilibrium points, and that positive risk management for both parties is a stable evolutionary strategy. The factors influencing the evolution results include the cost of positive risk management, risk perception loss and its share ratio, risk perception loss discount coefficient, and negative penalty coefficient. The differences in risk perceptions and effect of prospect theory hinder the behaviors of both parties from evolving towards the optimal strategy. By means of a negative penalty, a strong reciprocal government strategy can effectively coordinate the risk behavior strategies of both parties. Based on the analysis, suggestions are proposed for strengthening the effective management of risks in the construction stages of engineering projects.INDEX TERMS Engineering project, risk management behavior, strong reciprocity theory, prospect theory, evolutionary game.