We consider global games with general payoff structures and prove existence of equilibrium. This shows that the global games’ method is well defined with arbitrary strategic interaction among players, thus providing a foundation for the study of more general equilibrium behavior, especially as research in global games moves beyond the case of strategic complements. We also show that, in every global game, even though the information of each player is correlated, the joint information measure is absolutely continuous with respect to the product of its marginals. As one application, the result here can be used to show the existence of equilibrium in global games with both complementarity and congestion. This proves existence of equilibrium in a finite-player version of the model in Karp et al. (Games Econ Behav 60:155–175, 2007), thus addressing a gap in the proof of equilibrium existence documented in Hoffmann and Sabarwal (Games Econ Behav 94:188–190, 2015).