This paper studies binary response static games of complete information allowing complex heterogeneity through a random coefficients specification. The main result of the paper establishes nonparametric point identification of the joint density of all random coefficients except those on interaction effects. Under additional independence assumptions, we identify the joint density of the interaction coefficients as well. Moreover, we prove that in the presence of covariates that are common to both players, the player-specific coefficient densities are identified, while the joint density of all random coefficients is not point identified. However, we do provide bounds on counterfactual probabilities that involve this joint density.