Much of what we do as humans is engage socially with other agents, a skill that robots must also eventually possess. We demonstrate that a rich theory of social interactions originating from microsociology can be formalized by extending a nested MDP where agents reason about arbitrary functions of each other's rewards. This extended Social MDP allows us to encode the five basic interactions that underlie microsociology: cooperation, conflict, coercion, competition, and exchange. The result is a robotic agent capable of executing social interactions in new environments with no interaction-specific training; like humans it can engage socially in novel ways even without a single example of that social interaction. Moreover, the estimations of these Social MDPs align closely with the judge-ments of humans when considering which social interaction is taking place in an environment. This method both sheds light on the nature of social interactions, by providing concrete mathematical definitions, and brings rich social interactions into a mathematical framework that has proven to be natural for robotics.