<p>Housing markets carry various risks (e.g., price bubbles and bursts, interest rate fluctuations, economic downturns, natural disasters, climate change, and policy risks). This study assumes that uncertainty affects the decisions using a Wiener process in the evolution of the dynamical system of housing markets. It investigates the profit of housing investment for cooperative and non-cooperative games considering a stochastic differential game framework, the effect of uncertainty in housing characteristics on housing prices, social optimum, and Nash equilibrium solutions. Hence, this study offers a stochastic differential game for housing markets, where buyers and investors are engaged in a dynamic stochastic environment to invest in housing by considering its characteristics in their investment decision to buy a house. The study illustrates the effectiveness of the results with numerical simulations. The results show that the game theory can be used to detect the effect of house characteristics on housing prices.</p>