With the advancement of urbanisation, the inflow of population in China’s large cities has been increasing and the demand for rental housing of “new citizens” with insufficient housing affordability has become increasingly strong. Therefore, the Chinese government proposes to provide government-subsidized rental housing (GSRH) different from public rental housing. At present, the supply mode of public rental housing in China is mainly government construction and operation, which has the problems of low supply efficiency and low service level. It is critical to explore an efficient supply model in the construction of the GSRH system. Therefore, this study, starting from the three supply subjects of government, market, and society, constructs an evolutionary game model and uses agent-based modelling simulation to explore how multisubjects achieve optimal collaboration in the supply process of GSRH. The results are as follows: First, the development of a collaborative supply system includes four stages: noncooperative behaviour, collaborative exploration, collaborative game, and three-subject collaborative supply. Second, the government is the core of realising multisubject coordination. Increasing government supervision will boost market participation, while increasing government subsidies can fully mobilise the enthusiasm of social subjects but cannot continuously improve the market’s enthusiasm. Third, increasing the participation ratio of social subjects will help mobilise the enthusiasm of other subjects to participate, while the excessive participation ratio of market subjects may cause an imbalance in the collaborative supply system. This study provides theoretical support for the efficient supply of GSRH.