This paper investigates a pollution control model with incomplete information, in which different countries simultaneously aim to determine the optimal investment allocation in environmental projects and the tolerable pollutant emissions so as to maximize their welfare. Damage deriving from pollution of each country could be considered as a continuous random variable due to the influence of atmospheric and geologic factors that countries cannot really control. The equilibrium concept governing the model is that of Bayesian Nash equilibrium, which is given as a solution of a variational inequality in a Hilbert space. The existence of solutions is investigated.