Green construction is an important direction for the future of the construction industry, while developing green buildings is an effective way to reduce greenhouse gas emissions. Designing an incentive mechanism for green building projects is one of the main contents of project management research. However, traditional game models or evolutionary game models cannot consider the symbiotic changes of the number of different populations at the same time when studying the mechanism of the interaction between them. Aiming to solve this problem on the basis of the density game theory by taking into account the limited capacity for green and traditional buildings in the micro-market, the symbiosis equation and game payoff matrix for green and traditional building projects are combined, and an independent symbiosis density game model of green and traditional buildings is proposed. The stability of the model is analyzed using the stability theory of ordinary differential equations. Furthermore, the dynamic characteristics of different populations in the game model considering the payoff matrix are simulated using the system dynamics software Vensim.
It is discovered that there is a unique symbiotic stability point in the model, which is related to the market capacity and game payoff matrix. The stability condition of our model is closely relevant to the payoff matrix for green and traditional buildings, but has nothing to do with the net replication rate of green and traditional buildings. The effectiveness of policy incentives is closely related to the behavior choice by the micro agents. The simulation results based on the real case from China show that the model can reveal and explain the symbiotic developing process for green and traditional buildings in China. The model and simulation results can also provide effective technical support and theoretical basis for promoting the development of green buildings, and can offer a good reference for other decision-making problems that need to consider both population symbiosis and mutual games.