When humans share space in road traffic, as drivers or as vulnerable road users, they draw on their full range of communicative and interactive capabilities. Much remains unknown about these behaviors, but they need to be captured in models if automated vehicles are to coexist successfully with human road users. Empirical studies of human road user behavior implicate a large number of underlying cognitive mechanisms, which taken together are well beyond the scope of existing computational models. Here, we note that for all of these putative mechanisms, computational theories exist in different subdisciplines of psychology, for more constrained tasks. We demonstrate how these separate theories can be generalized from abstract laboratory paradigms and integrated into a computational framework for modeling human road user interaction, combining Bayesian perception, a theory of mind regarding others’ intentions, behavioral game theory, long-term valuation of action alternatives, and evidence accumulation decision-making. We show that a model with these assumptions—but not simpler versions of the same model—can account for a number of previously unexplained phenomena in naturalistic driver–pedestrian road-crossing interactions, and successfully predicts interaction outcomes in an unseen data set. Our modeling results contribute to demonstrating the real-world value of the theories from which we draw, and address calls in psychology for cumulative theory-building, presenting human road use as a suitable setting for work of this nature. Our findings also underscore the formidable complexity of human interaction in road traffic, with strong implications for the requirements to set on development and testing of vehicle automation.