  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 and economics can be
formalized by extending a nested MDP where agents reason about arbitrary
functions of each other's hidden 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 zero-shot in new environments; like
humans it can engage socially in novel ways even without a single example of
that social interaction. Moreover, the judgments of these Social MDPs align
closely with those 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, MDPs.
