This article draws on earlier work in social system theorizing and analysis-in particular, the theory of social rule systems. On the basis of this foundational work, its aim is to systematically link theories of social groups and organizations, on the one hand, and social science game and interaction theory, on the other hand. Rule system theory has contributed to significant features of group theory and social science game theory. It is a cultural-institutional approach to conceptualizing group systems and games. We explore how groups and their particular games can be effectively described, analyzed, and compared-and their similarities and differences identified on a systematic basis. For illustrative purposes, we present a selection of several ideal types of groups: a military unit, a terrorist group, a recreational or social group, a research group, and a business entity, each of whom has a distinct rule configuration making for particular "rules of the game" and game patterns of interaction and outcome.